Exercise 9 Page 89

To solve an equation with all of the variable terms on one side, we will combine like terms. We will start by expanding fractions, so that they have the same denominators.

4/9x + 1/5x = 87

ExpandFrac

a/b=a * 5/b * 5

4 * 5/9 * 5x + 1/5x = 87

ExpandFrac

a/b=a * 9/b * 9

4 * 5/9 * 5x + 1 * 9/5 * 9x = 87

Multiply

Multiply

20/45x + 9/45x = 87

AddFrac

Add fractions

29/45x = 87

MultEqn

LHS * 45/29=RHS* 45/29

45/29 * 29/45x = 45/29 * 87

MultFracByInverse

a/b* b/a=1

x = 45/29 * 87

▼

Simplify right-hand side

MoveRightFacToNum

a/c* b = a* b/c

x = 45 * 87/29

SplitIntoFactors

Split into factors

x = 45 * 3 * 29/29

CancelCommonFac

Cancel out common factors

x = 45 * 3 * 29/29

SimpQuot

Simplify quotient

x = 45 * 3

Multiply

Multiply

x = 135

The solution to the equation is x=135.