Big Ideas Math: Modeling Real Life, Grade 7
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3. Solving Two-Step Equations
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Exercise 30 Page 143

Start by multiplying both sides by - 32.

x = -27/20

Practice makes perfect
To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the Properties of Equality. In this case, the only variable term is already on the left-hand side of the equation, so we will start by multiplying both sides by - 32. We do it because multiplying by the reciprocal will eliminate the fraction.
- 2/3(x+ 3/5 )=1/2
- 2/3(x+ 3/5 )( - 3/2)= 1/2( - 3/2)
â–Ľ
Simplify left-hand side
- 2/3( - 3/2)(x+ 3/5 )= 1/2( - 3/2)
2/3( 3/2)(x+ 3/5 )= 1/2( - 3/2)
1(x+ 3/5 )=1/2( - 3/2)
(x+ 3/5 )= 1/2( - 3/2)
x+ 3/5= 1/2( - 3/2)
â–Ľ
Simplify right-hand side
x+ 3/5= 1/2( - 3/2)
x+ 3/5= 1(- 3)/2 * 2
x+ 3/5= - 3/4
x+ 3/5-3/5= - 3/4 -3/5
x= - 3/4 -3/5
To calculate the difference, we should make sure that both fractions have the same denominator. Because now the denominators are different, we will expand each fraction to create a common denominator of 20. Let's go!
x= - 3/4 -3/5
â–Ľ
Simplify right-hand side
x= - 3 * 5/4 * 5 -3/5
x= - 3 * 5/4 * 5 -3 * 4/5 * 4
x= - 15/20 -12/20
x= - 15-12/20
x= - 27/20
x = -27/20
x=- 1 720
The solution to the equation is x = - 2720, which can be also written as x=- 1 720. We can check our solution by substituting it into the original equation.
- 2/3(x+ 3/5 )=1/2
- 2/3( -27/20+ 3/5 ) ? =1/2
â–Ľ
Simplify
- 2/3(-27/20+ 3*4/5 * 4 ) ? =1/2
- 2/3(-27/20+ 12/20 ) ? =1/2
- 2/3(- 27/20+ 12/20 ) ? =1/2
- 2/3 * - 27+12/20 ? =1/2
- 2/3 * - 15/20 ? =1/2
- 2 * (- 15)/3 * 20 ? =1/2
30/60 ? =1/2
30/30/60/30 ? =1/2
1/2=1/2
Since the left-hand side is equal to the right-hand side, our solution is correct.