Exercise 2 Page 148

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, the variable terms are already on the left-hand side of the equation, so we will start by combining like terms.

21/4x+1/2x=44

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Add fractions

MixedToFrac

a bc=a* c+b/c

2* 4+ 1/4x+1/2x=44

ExpandFrac

a/b=a * 2/b * 2

2* 4+ 1/4x+1* 2/2* 2x=44

Multiply

Multiply

8+ 1/4x+2/4x=44

AddTerms

Add terms

9/4x+2/4x=44

MoveRightFacToNum

a/c* b = a* b/c

9x/4+2x/4=44

AddFrac

Add fractions

9x+2x/4=44

AddTerms

Add terms

11x/4=44

MultEqn

LHS * 4=RHS* 4

4* 11x/4=4* 44

DenomMultFracToNumber

4 * a/4= a

11x=44* 4

DivEqn

.LHS /11.=.RHS /11.

11x/11=44* 4/11

CancelCommonFac

Cancel out common factors

11x/11=44* 4/11

SimpQuot

Simplify quotient

x = 44* 4/11

ReduceFrac

a/b=.a /11./.b /11.

x = 4* 4/1

Multiply

Multiply

x = 16/1

DivByOne

a/1=a

x = 16

The solution to the equation is x=16.