Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=4 in expression 3x+5, write 3(4)+5 replacing x with 4, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: 3x+5 at x=4 becomes 3(4)+5, multiply first: 12, then add: 12+5=17. For this specific question, evaluate 3x+5 at x=4: substitute 3(4)+5, evaluate 3×4=12 (multiply), then 12+5=17 (add). Correct substitution and evaluation yield 17, which matches choice C. Common errors include concatenation (3x with x=4 as 34 instead of 3×4=12) or violating order by adding before multiplying (3+5=8, then 8×4=32). Process: (1) write expression 3x+5, (2) substitute x=4 to get 3(4)+5, (3) evaluate using order (multiply then add to get 17), (4) verify reasonable (3×4=12, +5=17 makes sense).

Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (for x=3 and y=4 in x²+y, write (3)²+(4), use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). With exponent: x²+y at x=3, y=4 becomes 3²+4, exponent: 9, add: 9+4=13. For this specific question, substitute x=3 and y=4 into x²+y: 3²+4, evaluate exponent 3²=9, then 9+4=13 (add). Correct substitution and evaluation yield 13, which matches choice A. Common errors include exponent as multiplication (3×2=6 +4=10) or not substituting both variables. Process: (1) write expression x²+y, (2) substitute to get 3²+4, (3) evaluate using order (exponent then add to get 13), (4) verify reasonable (3 squared=9, +4=13 makes sense).

This problem tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=5 and y=2 in expression 2x+3y, write 2(5)+3(2) replacing x with 5 and y with 2, use parentheses for clarity). To evaluate 2x+3y when x=5 and y=2, substitute: 2(5)+3(2), then evaluate: 2×5=10 and 3×2=6 (multiply first), then 10+6=16 (add). The correct answer is 16. Common errors include not substituting all variables (leaving answer as 10+3y), concatenation (reading 2x as 25), or arithmetic mistakes. Process: (1) write expression with variables (2x+3y), (2) substitute all given values (x=5, y=2: write 2(5)+3(2)), (3) evaluate using order (multiply: 2×5=10 and 3×2=6, add: 10+6=16), (4) verify reasonable (2×5=10, 3×2=6, sum=16✓).

Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=3 in 18-2x², write 18-2(3)², use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). With exponent: 18-2x² at x=3 becomes 18-2(3)², exponent: 9, multiply: 2×9=18, subtract: 18-18=0. For this specific question, evaluate 18-2x² at x=3: substitute 18-2(3)², exponent: 3²=9, multiply: 2×9=18, subtract: 18-18=0. Correct substitution and evaluation yield 0, which matches choice A. Common errors include order violations like subtracting before exponent (18-2=16, then 16×3²=144) or exponent wrong (3²=6). Process: (1) write expression 18-2x², (2) substitute x=3 to get 18-2(3)², (3) evaluate using order (exponent, multiply, subtract to get 0), (4) verify reasonable (2×9=18, 18-18=0 makes sense).

Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if n=7 in $C=5n+3$, write $5(7)+3$ replacing n with 7, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: $5n+3$ at n=7 becomes $5(7)+3$, multiply: $35$, add: $35+3=38$. For this specific question, evaluate $C=5n+3$ at n=7: substitute $5(7)+3$, evaluate $5×7=35$ (multiply), then $35+3=38$ (add). Correct substitution and evaluation yield 38, which matches choice A. Real-world: cost formula $5n+3$ at n=7 items gives $5(7)+3=38$ dollars (substitute n, evaluate, interpret as cost). Process: (1) write expression $5n+3$, (2) substitute n=7 to get $5(7)+3$, (3) evaluate using order (multiply then add to get 38), (4) verify reasonable ($5×7=35$, +3=38 makes sense).

Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (for x=5 and y=2 in 2x+3y, write 2(5)+3(2), use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Two variables: 2x+3y at x=5, y=2 becomes 2(5)+3(2)=10+6=16. For this specific question, substitute x=5 and y=2 into 2x+3y: 2(5)+3(2), evaluate 2×5=10 and 3×2=6 (multiply), then 10+6=16 (add). Correct substitution and evaluation yield 16, which matches choice A. Common errors include not substituting all variables (leaving as 10+3y) or arithmetic mistakes (10+6=15). Process: (1) write expression 2x+3y, (2) substitute values to get 2(5)+3(2), (3) evaluate using order (multiplies then add to get 16), (4) verify reasonable (2×5=10, 3×2=6, total 16 makes sense).

This problem tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=6 in expression $3x+2$, write $3(6)+2$ replacing x with 6, use parentheses for clarity). To verify if $3x+2=20$ when x=6, substitute: $3(6)+2$, then evaluate: $3 \times 6 = 18$ (multiply first), then $18 + 2 = 20$ (add). Since $3(6)+2=20$, the equation is true when x=6, so the answer is "Yes, because $3(6)+2=20$". Common errors include concatenation (reading 3x as 36, giving $36+2=38$), wrong order (adding before multiplying), or arithmetic mistakes ($18+2=19$). Process: (1) substitute x=6 into $3x+2$, (2) evaluate $3(6)+2=18+2=20$, (3) compare to given value 20, (4) they match, so verification is correct.

This question tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=3 and y=4 in expression x²+2y, write 3²+2(4) replacing x and y, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: x²+2y at x=3, y=4 becomes 3²+2(4), exponent: 9, multiply: 8, add: 9+8=17. Two variables: track separately, substitute all. Specific evaluation: x²+2y at x=3, y=4, substitute: 3²+2(4), evaluate: 9+8=17. Common error: treating exponent as multiplication, like 3×2+8=14, but wrong.

Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=8 in (x+6)/2, write (8+6)/2, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: (x+6)/2 at x=8 becomes (8+6)/2, parentheses: 14, divide: 14/2=7. For this specific question, evaluate (x+6)/2 at x=8: substitute (8+6)/2, parentheses first: 8+6=14, then divide: 14/2=7. Correct substitution and evaluation yield 7, which matches choice C. Common errors include ignoring parentheses (8+6/2=8+3=11) or arithmetic mistakes (14/2=6). Process: (1) write expression (x+6)/2, (2) substitute x=8 to get (8+6)/2, (3) evaluate using order (parentheses then divide to get 7), (4) verify reasonable (8+6=14, half is 7 makes sense).

This question tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if $x=8$ in expression $(x+6)/2$, write $(8+6)/2$ replacing x with 8, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: $(x+6)/2$ at $x=8$ becomes $(8+6)/2$, parentheses: 14, divide: $14/2=7$. With exponent: $x^2 - 5$ at $x=4$ = $16-5=11$. Two variables: $2x+3y$ at $x=5$, $y=2$ = $10+6=16$. Specific evaluation: $(x+6)/2$ at $x=8$, substitute: $(8+6)/2$, evaluate: $14/2=7$.