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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

Chapter Review

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Exercise 13 Page 34

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

p = - 26

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, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

2(3 - p) - 17 = 41

Distribute 2

6 - 2p - 17 = 41

CommutativePropAdd

Commutative Property of Addition

- 2p + 6 - 17 = 41

Subtract term

- 2p - 11 = 41

Now, we can continue to solve using the Properties of Equality.

- 2p - 11 = 41

LHS+11=RHS+11

- 2p - 11 + 11 = 41 + 11

Add terms

- 2p = 52

.LHS /(- 2).=.RHS /(- 2).

- 2p/- 2 = 52/- 2

CancelCommonFac

Cancel out common factors

- 2p/- 2 = 52/- 2

Simplify quotient

p = 52/- 2

MoveNegDenomToFrac

Put minus sign in front of fraction

p = - 52/2

Calculate quotient

p = - 26

The solution to the equation is p = - 26. We can check our solution by substituting it into the original equation.

2(3 - p) - 17 = 41

p= - 26

2(3 - ( - 26)) - 17 ? = 41

a-(- b)=a+b

2(3 + 26) - 17 ? = 41

Add terms

2(29) - 17 ? = 41

Multiply

58 - 17 ? = 41

Subtract terms

41 = 41 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct.

Subchapter links

1 Solving Simple Equations p.33

2 Solving Multi-Step Equations p.34

3 Solving Equations with Variables on Both Sides p.34-35

4 Rewriting Equations and Formulas p.35