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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

3. Graphing Proportional Relationships

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Exercise 6 Page 159

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

x = - 9/2

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(1 - x) = 11

Distribute 2

2 - 2x = 11

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

2 - 2x = 11

LHS-2=RHS-2

2 - 2x - 2 = 11 - 2

Subtract term

- 2x = 9

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

- 2x/- 2=9/- 2

Calculate quotient

x = 9/- 2

MoveNegDenomToFrac

Put minus sign in front of fraction

x = - 9/2

The solution to the equation is x=- 92. We can check our solution by substituting it into the original equation.

2(1 - x) = 11

x= - 9/2

2(1 - ( - 9/2)) ? = 11

▼

Simplify

a-(- b)=a+b

2(1 + 9/2) ? = 11

Rewrite 1 as 2/2

2(2/2 + 9/2) ? = 11

Add and subtract terms

2* 11/2? = 11

DenomMultFracToNumber

2 * a/2= a

11 = 11 ✓

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

Subchapter links

Try It p.156-157

Self-Assessment for Concepts & Skills p.157

Self-Assessment for Problem Solving p.158

Review & Refresh p.159

Concepts, Skills, & Problem Solving p.159-160