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Pearson Algebra 1 Common Core, 2011 View details

3. Solving Multi-Step Equations

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Exercise 29 Page 98

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

9.75 or 9 34

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side of the equation 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.

-4(r+6)=-63

Distr

Distribute -4

(-4)r+(-4)6=-63

MultNegPos

(- a)b = - ab

-4r-24=-63

AddEqn

LHS+24=RHS+24

-4r-24+24=-63+24

AddTerms

Add terms

-4r=-39

DivEqn

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

r=-39/-4

DivNegNeg

- a/- b=a/b

r=39/4

The solution to the equation is r= 394. We can check our solution by substituting it into the original equation.

-4(r+6)=-63

Substitute

r= 39/4

-4( 39/4+6)? =-63

▼

Evaluate left-hand side

NumberToFrac

a = 4* a/4

-4(39/4+4* 6/4)? =-63

Multiply

-4(39/4+24/4)? =-63

AddFrac

Add fractions

-4(39+24/4)? =-63

AddTerms

Add terms

-4(63/4)? =-63

DenomMultFracToNumber

4 * a/4= a

-63=-63

Since the left-hand side is equal to the right-hand side, our solution is correct. Although r= 394 is a perfectly valid solution, we can also rewrite it as a mixed number.

r=39/4

WriteSum

Write as a sum

r=36+3/4

WriteSumFrac

Write as a sum of fractions

r=36/4+3/4

CalcQuot

Calculate quotient

r=9+3/4

Rewrite

Rewrite 9+3/4 as 9 34