Core Connections Geometry, 2013
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Core Connections Geometry, 2013 View details
2. Section 10.2
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Exercise 89 Page 619

Practice makes perfect
a To solve the given equation let's use the inverse operations in order to isolate x. In this case, we should multiply both sides of the equation by 2.

x/2 = 17 x = 34

Checking Our Answer

In order to check whether our answer is correct, we should substitute our solution for x in the original equation. If the result is a true equality, our solution is correct.
x/2 = 17
34/2 ? = 17
17 = 17 âś“
Since we got a true statement, our solution is correct.
b Like in Part A, to solve the given equation let's use the inverse operations in order to isolate x. In this case, we should multiply both sides of the equation by 4.

x/4 = 1/3 x = 4/3

Checking Our Answer

In order to check whether our answer is correct, we should substitute our solution for x in the original equation. If the result is a true equality, our solution is correct.
x/4 = 1/3
4/3/4 ? = 1/3
4/12? = 1/3
1/3 = 1/3 âś“
Since we got a true statement, our solution is correct.
c Like in Parts A-B, let's use the inverse operations in order to isolate x. Here, we should first subtract 2 from both sides of the equation.
x+6/2+2=5/2
x+6/2=5/2-2
x+6/2=5/2-4/2
x+6/2=1/2
x+6 = 1
x = -5

Checking Our Answer

In order to check whether our answer is correct, we should substitute our solution for x in the original equation. If the result is a true equality, our solution is correct.
x+6/2+2=5/2
-5+6/2+2? =5/2
1/2+2? =5/2
1/2+4/2? =5/2
5/2=5/2 âś“
Since we got a true statement, our solution is correct.
d To solve the proportion, we will start by using cross products. Remember that since we start with x being the denominator of one of the fractions, 0 cannot be a solution to our equation.
4/x = 5/8
4(8) = 5x
32 = 5x
32/5=x
x = 32/5

Checking Our Answer

In order to check whether our answer is correct, we should substitute our solution for x in the original equation. If the result is a true equality, our solution is correct.
4/x = 5/8
4/32/5 ? = 5/8
20/32? = 5/8
5/8 = 5/8 âś“
Since we got a true statement, our solution is correct.