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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

4. Solving Equations With Variables on Both Sides

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Exercise 17 Page 105

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

c=-1 34

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.

-3c-12=-5+c

LHS-c=RHS-c

-3c-12-c=-5+c-c

Subtract terms

-4c-12=-5

LHS+12=RHS+12

-4c-12+12=-5+12

Add terms

-4c=7

.LHS /(-4).=.RHS /(-4).

-4c/-4=7/-4

Calculate quotient

c=7/-4

MoveNegDenomToFrac

Put minus sign in front of fraction

c=-7/4

The solution to the equation is c=- 74. We can check our solution by substituting it into the original equation.

-3c-12=-5+c

c= -7/4

-3 ( -7/4)-12? =-5+( -7/4)

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Simplify

MoveNegFracToNum

Put minus sign in numerator

-3 (- 7/4)-12 ? =-5+(- 7/4)

MoveLeftFacToNum

a*b/c= a* b/c

(-3)(- 7)/4-12 ? =-5+(- 7/4)

MultNegNegTwoPar

(- a)(- b)=a* b

21/4-12? =-5+(- 7/4)

a = 4* a/4

21/4-12* 4/4? =-5 * 4/4+(- 7/4)

Multiply

21/4-48/4? =-20/4+(- 7/4)

MoveNegNumToFrac

Put minus sign in front of fraction

21/4-48/4? =-20/4-7/4

Subtract fractions

21-48/4? =-20-7/4

Subtract terms

-27/4=-27/4 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct. We can also show our answer as a mixed number.

-7/4

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Write as mixed number

Rewrite 7 as 4+3

-4+3/4

Add parentheses

-(4+3/4)

Write as a sum of fractions

-(4/4+3/4)

a/a=1

-(1+3/4)

Add terms

-(1 34)

Remove parentheses

-1 34

Subchapter links

Lesson Check p.105

Practice and Problem-Solving Exercises p.105-108

Standardized Test Prep p.108

Mixed Review p.108