Add, Subtract, Factor Linear Expressions - 7th Grade Math
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What is the GCF factoring form for two terms $ax+ay$?
What is the GCF factoring form for two terms $ax+ay$?
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$ax+ay=a(x+y)$. Factor out the common factor $a$ from both terms.
$ax+ay=a(x+y)$. Factor out the common factor $a$ from both terms.
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What is the rule for distributing a negative sign: $-(a-b)$?
What is the rule for distributing a negative sign: $-(a-b)$?
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$-(a-b)=-a+b$. Negative sign changes both signs inside parentheses.
$-(a-b)=-a+b$. Negative sign changes both signs inside parentheses.
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What is the rule for subtracting an expression, written as $a-(b+c)$?
What is the rule for subtracting an expression, written as $a-(b+c)$?
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$a-(b+c)=a-b-c$. Distribute the negative sign to both terms inside parentheses.
$a-(b+c)=a-b-c$. Distribute the negative sign to both terms inside parentheses.
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What property is shown by $(a+b)+c=a+(b+c)$ when regrouping terms?
What property is shown by $(a+b)+c=a+(b+c)$ when regrouping terms?
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Associative property of addition. Grouping of addends doesn't change the sum.
Associative property of addition. Grouping of addends doesn't change the sum.
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What property is shown by $ab=ba$ when rewriting a product in a different order?
What property is shown by $ab=ba$ when rewriting a product in a different order?
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Commutative property of multiplication. Order of factors doesn't change the product.
Commutative property of multiplication. Order of factors doesn't change the product.
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What property is shown by $a(b+c)=ab+ac$ when expanding expressions?
What property is shown by $a(b+c)=ab+ac$ when expanding expressions?
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Distributive property. Multiplying a factor by a sum equals the sum of the products.
Distributive property. Multiplying a factor by a sum equals the sum of the products.
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What is the result of expanding $3(2x-5)$?
What is the result of expanding $3(2x-5)$?
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$6x-15$. Multiply 3 by each term: $3(2x) - 3(5)$.
$6x-15$. Multiply 3 by each term: $3(2x) - 3(5)$.
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What is the identity for combining like terms $kx+mx$?
What is the identity for combining like terms $kx+mx$?
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$kx+mx=(k+m)x$. Combine coefficients of the same variable.
$kx+mx=(k+m)x$. Combine coefficients of the same variable.
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What is the simplified form of $5x-2x+7$?
What is the simplified form of $5x-2x+7$?
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$3x+7$. Combine like terms: $(5-2)x + 7$.
$3x+7$. Combine like terms: $(5-2)x + 7$.
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What is the simplified form of $4x+3-2x-9$?
What is the simplified form of $4x+3-2x-9$?
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$2x-6$. Combine like terms: $(4-2)x + (3-9)$.
$2x-6$. Combine like terms: $(4-2)x + (3-9)$.
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What is the result of expanding $\frac{3}{4}(8x+12)$?
What is the result of expanding $\frac{3}{4}(8x+12)$?
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$6x+9$. Multiply $\frac{3}{4}$ by each term: $\frac{3 \cdot 8x}{4} + \frac{3 \cdot 12}{4}$
$6x+9$. Multiply $\frac{3}{4}$ by each term: $\frac{3 \cdot 8x}{4} + \frac{3 \cdot 12}{4}$
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What is the factored form of $-6x-9$ using the GCF $-3$?
What is the factored form of $-6x-9$ using the GCF $-3$?
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$-3(2x+3)$. Factor out -3 from both negative terms.
$-3(2x+3)$. Factor out -3 from both negative terms.
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What is the expanded form of $\frac{1}{2}(6x-8)$?
What is the expanded form of $\frac{1}{2}(6x-8)$?
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$3x-4$. Distribute $\frac{1}{2}$: $\frac{1}{2}(6x) + \frac{1}{2}(-8) = 3x - 4$.
$3x-4$. Distribute $\frac{1}{2}$: $\frac{1}{2}(6x) + \frac{1}{2}(-8) = 3x - 4$.
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What is the simplified form of $3(x-2)+2(x+5)$?
What is the simplified form of $3(x-2)+2(x+5)$?
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$5x+4$. Distribute, then combine: $3x - 6 + 2x + 10 = 5x + 4$.
$5x+4$. Distribute, then combine: $3x - 6 + 2x + 10 = 5x + 4$.
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What property is shown by $a+b=b+a$?
What property is shown by $a+b=b+a$?
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Commutative property of addition. Order doesn't matter when adding terms.
Commutative property of addition. Order doesn't matter when adding terms.
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What is the simplified form of $2x+3-5x+1$?
What is the simplified form of $2x+3-5x+1$?
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$-3x+4$. Combine like terms: $2x - 5x = -3x$ and $3 + 1 = 4$.
$-3x+4$. Combine like terms: $2x - 5x = -3x$ and $3 + 1 = 4$.
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What is the simplified form of $6-2(3x-4)$?
What is the simplified form of $6-2(3x-4)$?
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$-6x+14$. Distribute $-2$, then combine: $6 - 6x + 8 = -6x + 14$.
$-6x+14$. Distribute $-2$, then combine: $6 - 6x + 8 = -6x + 14$.
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What is the simplified form of $\frac{3}{4}x+\frac{1}{2}x$?
What is the simplified form of $\frac{3}{4}x+\frac{1}{2}x$?
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$\frac{5}{4}x$. Add fractions: $\frac{3}{4} + \frac{2}{4} = \frac{5}{4}$.
$\frac{5}{4}x$. Add fractions: $\frac{3}{4} + \frac{2}{4} = \frac{5}{4}$.
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What is the simplified form of $\frac{2}{3}x-\frac{1}{6}x$?
What is the simplified form of $\frac{2}{3}x-\frac{1}{6}x$?
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$\frac{1}{2}x$. Subtract fractions: $\frac{4}{6} - \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$.
$\frac{1}{2}x$. Subtract fractions: $\frac{4}{6} - \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$.
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What is the simplified form of $-(x-7)$?
What is the simplified form of $-(x-7)$?
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$-x+7$. Distribute $-1$: $-1(x) + (-1)(-7) = -x + 7$.
$-x+7$. Distribute $-1$: $-1(x) + (-1)(-7) = -x + 7$.
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What is the simplified form of $-(2x+5)+3x$?
What is the simplified form of $-(2x+5)+3x$?
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$x-5$. Distribute $-1$, then combine: $-2x - 5 + 3x = x - 5$.
$x-5$. Distribute $-1$, then combine: $-2x - 5 + 3x = x - 5$.
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What is the factored form of $9x+12$ using the GCF?
What is the factored form of $9x+12$ using the GCF?
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$3(3x+4)$. Factor out GCF of 3: $3(3x) + 3(4) = 3(3x + 4)$.
$3(3x+4)$. Factor out GCF of 3: $3(3x) + 3(4) = 3(3x + 4)$.
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What property is shown by $a(b+c)=ab+ac$?
What property is shown by $a(b+c)=ab+ac$?
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Distributive property. Multiplying a term by a sum equals the sum of the products.
Distributive property. Multiplying a term by a sum equals the sum of the products.
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What is the factored form of $\frac{5}{6}x+\frac{5}{3}$ using the GCF?
What is the factored form of $\frac{5}{6}x+\frac{5}{3}$ using the GCF?
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$\frac{5}{6}(x+2)$. Factor out GCF of $\frac{5}{6}$: $\frac{5}{6}(x + 2)$.
$\frac{5}{6}(x+2)$. Factor out GCF of $\frac{5}{6}$: $\frac{5}{6}(x + 2)$.
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What is the simplified form of $4(x+3)$?
What is the simplified form of $4(x+3)$?
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$4x+12$. Distribute: $4 \cdot x + 4 \cdot 3 = 4x + 12$.
$4x+12$. Distribute: $4 \cdot x + 4 \cdot 3 = 4x + 12$.
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