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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 5 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=23/18

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.

x + 1/6 = 4 - 2x

LHS+2x=RHS+2x

3x + 1/6 = 4

LHS-1/6=RHS-1/6

3x = 4 - 1/6

a = 6* a/6

3x = 24/6 - 1/6

Subtract fractions

3x = 23/6

Now, we will use the Division Property of Equality.

3x = 23/6

.LHS /3.=.RHS /3.

x = 23/6/3

a/c/b= a/b* c

x = 23/6* 3

Multiply

x = 23/18

The solution to the equation is x= 2318. We can check our solution by substituting it into the original equation.

x + 1/6 = 4 - 2x

x= 23/18

23/18 + 1/6 ? = 4 - 2 * 23/18

▼

Simplify

Multiply

23/18 + 1/6 ? = 4 - 46/18

a/b=.a /2./.b /2.

23/18 + 1/6 ? = 4 - 23/9

a/b=a * 3/b * 3

23/18 + 3/18 ? = 4 - 23/9

a = 9* a/9

23/18 + 3/18 ? = 36/9 - 23/9

Add and subtract fractions

26/18? =13/9

a/b=.a /2./.b /2.

13/9 = 13/9 ✓

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