This question tests adding, subtracting, factoring, and expanding linear expressions with rational coefficients using properties of operations. Operations: add by combining like terms (3x+2x=5x, coefficients add), subtract by distributing negative then combining (4x-(2x-3)=4x-2x+3=2x+3, negative distributes to all terms), expand using distributive property a(b+c)=ab+ac (multiply each term: 3(2x-5)=6x-15), factor by finding GCF and dividing out (6x+9: GCF=3, so 3(6x/3+9/3)=3(2x+3)). Combining like terms requires same variable (3x and 5x combine, but 2x and 3 don't). For example, (2x - 3/4) + (-5x + 1/2) combines x terms (2 - 5 = -3x) and constants (-3/4 + 2/4 = -1/4), giving -3x - 1/4. In this case, the correct simplification is -3x - 1/4. A common error is sign error in adding fractions without a common denominator, such as -3/4 + 1/2 = -3/4 + 1/2 = 1/4 instead of -1/4. Strategy: (1) for adding/subtracting: distribute any negatives first (important for subtraction), identify like terms (same variable part: 3x and 5x are like, 2x and 3 aren't), combine (add/subtract coefficients: 3x+5x=8x), combine constants separately (5-3=2); (2) for expanding: distribute to every term (a(b+c+d)=ab+ac+ad, don't miss any); (3) for factoring: find GCF of all terms, divide each term by GCF, write as GCF(quotients). Common mistakes: distributing negative to only first term -(2x-3)=-2x-3 (wrong, should be -2x+3), combining unlike terms, fraction operations without common denominators, factoring incompletely.

This question tests adding, subtracting, factoring, and expanding linear expressions with rational coefficients using properties of operations. Operations include adding by combining like terms (3x+2x=5x, coefficients add), subtracting by distributing the negative then combining (4x-(2x-3)=4x-2x+3=2x+3, negative distributes to all terms), expanding using the distributive property a(b+c)=ab+ac (multiply each term: 3(2x-5)=6x-15), and factoring by finding the GCF and dividing out (6x+9: GCF=3, so 3(6x/3+9/3)=3(2x+3)). Combining like terms requires the same variable (3x and 5x combine, but 2x and 3 don't). For example, (3x+5)+(2x-3) combines like terms: 3x+2x=5x, 5+(-3)=2, giving 5x+2; or (4x+7)-(2x+3) distributes the negative: 4x+7-2x-3, combines to 2x+4; or factor 8x+12: GCF=4, so 4(2x+3). Factor completely by finding GCF 6: 12x/6 = 2x, 18/6 = 3, giving 6(2x + 3), which is choice A. A common error is factoring partially, like pulling out only 3 to get 3(4x + 6) without checking for a larger GCF. Strategy: (1) for adding/subtracting: distribute any negatives first (important for subtraction), identify like terms (same variable part: 3x and 5x are like, 2x and 3 aren't), combine (add/subtract coefficients: 3x+5x=8x), combine constants separately (5-3=2); (2) for expanding: distribute to every term (a(b+c+d)=ab+ac+ad, don't miss any); (3) for factoring: find GCF of all terms, divide each term by GCF, write as GCF(quotients). Common mistakes: distributing negative to only first term -(2x-3)=-2x-3 (wrong, should be -2x+3), combining unlike terms, fraction operations without common denominators, factoring incompletely.

This question tests adding, subtracting, factoring, and expanding linear expressions with rational coefficients using properties of operations. Operations include adding by combining like terms (3x+2x=5x, coefficients add), subtracting by distributing the negative then combining (4x-(2x-3)=4x-2x+3=2x+3, negative distributes to all terms), expanding using the distributive property a(b+c)=ab+ac (multiply each term: 3(2x-5)=6x-15), and factoring by finding the GCF and dividing out (6x+9: GCF=3, so 3(6x/3+9/3)=3(2x+3)). Combining like terms requires the same variable (3x and 5x combine, but 2x and 3 don't). A specific example is (4x+7)-(2x+3): distribute negative 4x+7-2x-3, combine 2x+4. For this problem, distribute negative: 1.2x - 4.8 - 0.7x - 1.5, combine x terms: 1.2x - 0.7x = 0.5x, constants: -4.8 - 1.5 = -6.3, giving 0.5x - 6.3. A common error is sign error in subtraction, like not distributing the negative to the constant term. Strategy: for adding/subtracting, distribute any negatives first (important for subtraction), identify like terms (same variable part: 3x and 5x are like, 2x and 3 aren't), combine (add/subtract coefficients: 3x+5x=8x), combine constants separately (5-3=2); common mistakes include distributing negative to only first term -(2x-3)=-2x-3 (wrong, should be -2x+3).

This question tests adding, subtracting, factoring, and expanding linear expressions with rational coefficients using properties of operations. Operations include adding by combining like terms (3x+2x=5x, coefficients add), subtracting by distributing the negative then combining (4x-(2x-3)=4x-2x+3=2x+3, negative distributes to all terms), expanding using the distributive property a(b+c)=ab+ac (multiply each term: 3(2x-5)=6x-15), and factoring by finding the GCF and dividing out (6x+9: GCF=3, so 3(6x/3+9/3)=3(2x+3)). Combining like terms requires the same variable (3x and 5x combine, but 2x and 3 don't). A specific example is ((rac{2}{3}x + 5)) + ((rac{1}{3}x - 2)): combine (rac{2}{3} + rac{1}{3} = x), 5-2=3, giving x+3. For this problem, combine x terms: (rac{2}{3}x + rac{1}{6}x = rac{4}{6}x + rac{1}{6}x = rac{5}{6}x), constants: 5 - 2 = 3, resulting in (rac{5}{6}x + 3). A common error is fraction addition without common denominator, like adding (rac{2}{3} + rac{1}{6}) as (rac{3}{9}) instead of (rac{5}{6}). Strategy: for adding/subtracting, distribute any negatives first (important for subtraction), identify like terms (same variable part: 3x and 5x are like, 2x and 3 aren't), combine (add/subtract coefficients: 3x+5x=8x), combine constants separately (5-3=2); common mistakes include fraction operations without common denominators.

This question tests adding, subtracting, factoring, and expanding linear expressions with rational coefficients using properties of operations. Operations include adding by combining like terms (3x+2x=5x, coefficients add), subtracting by distributing the negative then combining (4x-(2x-3)=4x-2x+3=2x+3, negative distributes to all terms), expanding using the distributive property a(b+c)=ab+ac (multiply each term: 3(2x-5)=6x-15), and factoring by finding the GCF and dividing out (6x+9: GCF=3, so 3(6x/3+9/3)=3(2x+3)). Combining like terms requires the same variable (3x and 5x combine, but 2x and 3 don't). For example, (3x+5)+(2x-3) combines like terms: 3x+2x=5x, 5+(-3)=2, giving 5x+2; or (4x+7)-(2x+3) distributes the negative: 4x+7-2x-3, combines to 2x+4; or factor 8x+12: GCF=4, so 4(2x+3). Expand by distributing 3: 3*(2/3)x = 2x, and 3*(-5) = -15, resulting in 2x - 15, which is choice A. A common error is incomplete distribution, like multiplying only the first term and forgetting the second, giving just 2x without -15. Strategy: (1) for adding/subtracting: distribute any negatives first (important for subtraction), identify like terms (same variable part: 3x and 5x are like, 2x and 3 aren't), combine (add/subtract coefficients: 3x+5x=8x), combine constants separately (5-3=2); (2) for expanding: distribute to every term (a(b+c+d)=ab+ac+ad, don't miss any); (3) for factoring: find GCF of all terms, divide each term by GCF, write as GCF(quotients). Common mistakes: distributing negative to only first term -(2x-3)=-2x-3 (wrong, should be -2x+3), combining unlike terms, fraction operations without common denominators, factoring incompletely.

This question tests adding, subtracting, factoring, and expanding linear expressions with rational coefficients using properties of operations. Operations: add by combining like terms (3x+2x=5x, coefficients add), subtract by distributing negative then combining (4x-(2x-3)=4x-2x+3=2x+3, negative distributes to all terms), expand using distributive property a(b+c)=ab+ac (multiply each term: 3(2x-5)=6x-15), factor by finding GCF and dividing out (6x+9: GCF=3, so 3(6x/3+9/3)=3(2x+3)). Combining like terms requires same variable (3x and 5x combine, but 2x and 3 don't). For example, expanding 3(2x-5) using the distributive property gives 32x - 35 = 6x - 15. In this case, the correct expansion is 3(2x-5)=6x-15. A common error is missing the distribution to the second term or mishandling the sign, such as 3*2x -5 =6x-5 instead of multiplying the 5 by 3. Strategy: (1) for adding/subtracting: distribute any negatives first (important for subtraction), identify like terms (same variable part: 3x and 5x are like, 2x and 3 aren't), combine (add/subtract coefficients: 3x+5x=8x), combine constants separately (5-3=2); (2) for expanding: distribute to every term (a(b+c+d)=ab+ac+ad, don't miss any); (3) for factoring: find GCF of all terms, divide each term by GCF, write as GCF(quotients). Common mistakes: distributing negative to only first term -(2x-3)=-2x-3 (wrong, should be -2x+3), combining unlike terms, fraction operations without common denominators, factoring incompletely.

This question tests adding, subtracting, factoring, and expanding linear expressions with rational coefficients using properties of operations. Operations: add by combining like terms (3x+2x=5x, coefficients add), subtract by distributing negative then combining (4x-(2x-3)=4x-2x+3=2x+3, negative distributes to all terms), expand using distributive property a(b+c)=ab+ac (multiply each term: 3(2x-5)=6x-15), factor by finding GCF and dividing out (6x+9: GCF=3, so 3(6x/3+9/3)=3(2x+3)). Combining like terms requires same variable (3x and 5x combine, but 2x and 3 don't). For example, 0.5x + 2.5 - 0.3x + 1.5 combines x terms (0.5 - 0.3 = 0.2x) and constants (2.5 + 1.5 = 4), giving 0.2x + 4. In this case, the correct simplification is 0.2x + 4. A common error is combining unlike terms or mishandling decimals, such as adding all numbers without grouping. Strategy: (1) for adding/subtracting: distribute any negatives first (important for subtraction), identify like terms (same variable part: 3x and 5x are like, 2x and 3 aren't), combine (add/subtract coefficients: 3x+5x=8x), combine constants separately (5-3=2); (2) for expanding: distribute to every term (a(b+c+d)=ab+ac+ad, don't miss any); (3) for factoring: find GCF of all terms, divide each term by GCF, write as GCF(quotients). Common mistakes: distributing negative to only first term -(2x-3)=-2x-3 (wrong, should be -2x+3), combining unlike terms, fraction operations without common denominators, factoring incompletely.

This question tests adding, subtracting, factoring, and expanding linear expressions with rational coefficients using properties of operations. Operations: add by combining like terms (3x+2x=5x, coefficients add), subtract by distributing negative then combining (4x-(2x-3)=4x-2x+3=2x+3, negative distributes to all terms), expand using distributive property a(b+c)=ab+ac (multiply each term: 3(2x-5)=6x-15), factor by finding GCF and dividing out (6x+9: GCF=3, so 3(6x/3+9/3)=3(2x+3)). Combining like terms requires same variable (3x and 5x combine, but 2x and 3 don't). For example, 5(x - 2/5) + 3x expands to 5x - 2 + 3x, then combines to 8x - 2. In this case, the correct simplification is 8x - 2. A common error is not distributing the 5 to the -2/5 term fully, such as leaving it as 5x - 2/5 + 3x. Strategy: (1) for adding/subtracting: distribute any negatives first (important for subtraction), identify like terms (same variable part: 3x and 5x are like, 2x and 3 aren't), combine (add/subtract coefficients: 3x+5x=8x), combine constants separately (5-3=2); (2) for expanding: distribute to every term (a(b+c+d)=ab+ac+ad, don't miss any); (3) for factoring: find GCF of all terms, divide each term by GCF, write as GCF(quotients). Common mistakes: distributing negative to only first term -(2x-3)=-2x-3 (wrong, should be -2x+3), combining unlike terms, fraction operations without common denominators, factoring incompletely.

This question tests adding, subtracting, factoring, and expanding linear expressions with rational coefficients using properties of operations. Operations: add by combining like terms (3x+2x=5x, coefficients add), subtract by distributing negative then combining (4x-(2x-3)=4x-2x+3=2x+3, negative distributes to all terms), expand using distributive property a(b+c)=ab+ac (multiply each term: 3(2x-5)=6x-15), factor by finding GCF and dividing out (6x+9: GCF=3, so 3(6x/3+9/3)=3(2x+3)). Combining like terms requires same variable (3x and 5x combine, but 2x and 3 don't). For example, to factor 3/5 x + 6/5, find the GCF of 3/5 and 6/5 which is 3/5, then 3/5 (x + 2). In this case, the correct factoring is 3/5 (x + 2). A common error is not identifying the full GCF for fractions or factoring incompletely, such as using 6/5 instead. Strategy: (1) for adding/subtracting: distribute any negatives first (important for subtraction), identify like terms (same variable part: 3x and 5x are like, 2x and 3 aren't), combine (add/subtract coefficients: 3x+5x=8x), combine constants separately (5-3=2); (2) for expanding: distribute to every term (a(b+c+d)=ab+ac+ad, don't miss any); (3) for factoring: find GCF of all terms, divide each term by GCF, write as GCF(quotients). Common mistakes: distributing negative to only first term -(2x-3)=-2x-3 (wrong, should be -2x+3), combining unlike terms, fraction operations without common denominators, factoring incompletely.

This question tests adding, subtracting, factoring, and expanding linear expressions with rational coefficients using properties of operations. Operations: add by combining like terms (3x+2x=5x, coefficients add), subtract by distributing negative then combining (4x-(2x-3)=4x-2x+3=2x+3, negative distributes to all terms), expand using distributive property a(b+c)=ab+ac (multiply each term: 3(2x-5)=6x-15), factor by finding GCF and dividing out (6x+9: GCF=3, so 3(6x/3+9/3)=3(2x+3)). Combining like terms requires same variable (3x and 5x combine, but 2x and 3 don't). For example, 5(x - 2/5) + 3x expands to 5x - 2 + 3x, then combines to 8x - 2. In this case, the correct simplification is 8x - 2. A common error is not distributing the 5 to the -2/5 term fully, such as leaving it as 5x - 2/5 + 3x. Strategy: (1) for adding/subtracting: distribute any negatives first (important for subtraction), identify like terms (same variable part: 3x and 5x are like, 2x and 3 aren't), combine (add/subtract coefficients: 3x+5x=8x), combine constants separately (5-3=2); (2) for expanding: distribute to every term (a(b+c+d)=ab+ac+ad, don't miss any); (3) for factoring: find GCF of all terms, divide each term by GCF, write as GCF(quotients). Common mistakes: distributing negative to only first term -(2x-3)=-2x-3 (wrong, should be -2x+3), combining unlike terms, fraction operations without common denominators, factoring incompletely.