Envision Math 2.0: Grade 7, Volume 1
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7. Subtract Expressions
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Exercise 4 Page 234

Practice makes perfect
a Before we try to simplify the given expression, let's use the Distributive Property so that we can get rid of the parentheses. This will also let us see the correct coefficients for any terms with variables.
(21x)-(-16+7x)
21x+(-1)(-16) + (-1)7x
21x+16 + (-1)7x
21x+16-7x
The next step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined. 21x+ 16 - 7x In this case, we have two x-terms and one constant. Only the x-terms can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition and then combine like terms.
21x+16-7x
21x-7x+16
14x+16
b Before we try to simplify the given expression, let's use the |Distributive Property so that we can get rid of the parentheses. This will also let us see the correct coefficients for any terms with variables.
(-13n)-(17-5n)
-13n+(-1)17+(-1)(-5n)
-13n-17+(-1)(-5n)
-13n-17+5n
The next step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined. -13n - 17+ 5n In this case, we have two n-terms and one constant. Only the n-terms can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition and then combine like terms.
-13n-17+5n
-13n+5n-17
-8n-17
c Before we try to simplify the given expression, let's use the |Distributive Property so that we can get rid of the parentheses. This will also let us see the correct coefficients for any terms with variables.
(4y-7)-(y-7)
4y-7+(-1)(y)+(-1)(-7)
4y-7-y+(-1)(-7)
4y-7-y+7
The next step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined. 4y - 7 - y + 7 In this case, we have two y-terms and two constants. Both the y-terms and the constants can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition and then combine like terms.
4y-7-y+7
4y-y-7+7
3y
d Before we try to simplify the given expression, let's use the |Distributive Property so that we can get rid of the parentheses. This will also let us see the correct coefficients for any terms with variables.
(- w + 0.4)-(- w -0.4)
- w + 0.4 +(-1)(- w) + (-1)(-0.4)
- w + 0.4 + w + 0.4
The next step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined. - w + 0.4 + w + 0.4 In this case, we have two w-terms and two constants. Both the w-terms and the constants can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition and then combine like terms.
- w + 0.4 + w + 0.4
- w + w+ 0.4 + 0.4
0.8