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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

1. Solving One-Step Equations

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Exercise 58 Page 86

Isolate g on one side of the equation.

- 6 34

Practice makes perfect

To solve the equation, we have to isolate g on one side. We will start by rewriting the mixed number as an improper fraction. Then, we will use the Multiplication Property of Equality and multiply both sides of the equation by the reciprocal of the coefficient of the variable g. This will eliminate the fraction and isolate g.

2/3g=-4 12

▼

Write mixed number as a fraction

a bc=a* c+b/c

2/3g=-4*2+1/2

Multiply

2/3g=-8+1/2

Add terms

2/3g=-9/2

LHS * 3/2=RHS* 3/2

2/3g * 3/2=-9/2 * 3/2

CommutativePropMult

Commutative Property of Multiplication

3/2 * 2/3 * g=-9/2 * 3/2

MultFracByInverse

a/b* b/a=1

1 * g=-9/2 * 3/2

Identity Property of Multiplication

g=-9/2 * 3/2

Multiply fractions

g=-9 * 3/2 * 2

Multiply

g=-27/4

Therefore, g=- 274 is the solution to the equation. To check that we have the correct solution, we can substitute g=- 274 into the original equation and simplify.

2/3g? =-4 12

▼

Write mixed number as a fraction

a bc=a* c+b/c

2/3g? =-4*2+1/2

Multiply

2/3g? =-8+1/2

Add terms

2/3g? =-9/2

g= -27/4

2/3* ( -27/4)? =-9/2

a(- b)=- a * b

-2/3*27/4? =-9/2

Multiply fractions

-2* 27/3* 4? =-9/2

Multiply

-54/12? =-9/2

a/b=.a /6./.b /6.

-54/6/12/6? =-9/2

Calculate quotient

-9/2=-9/2 ✓

Since the left-hand side and the right-hand side are equal, g=- 274 is the correct solution. However, we can also write our answer as a mixed number.

g=-27/4

▼

Write as mixed number

Rewrite 27 as 24+3

g=-24+3/4

Add parentheses

g=-(24+3/4)

Write as a sum of fractions

g=-(24/4+3/4)

Calculate quotient

g=-(6+3/4)

Finally, the numeric expression 6+ 34 can be read as 6 and 34. Therefore, it can be written as 6 34. y=-(6+3/4) ⇔ y=-6 34

Subchapter links

Lesson Check p.85

Practice and Problem-Solving Exercises p.85-87

Standardized Test Prep p.87

Mixed Review p.87