Exercise 1 Page 104

To solve an equation with a variable on both sides, we 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.

13x+2=4x+38

SubEqn

LHS-2=RHS-2

13x+2-2=4x+38-2

SubTerms

Subtract terms

13x=4x+36

SubEqn

LHS-4x=RHS-4x

13x-4x=4x+36-4x

SubTerms

Subtract terms

9x = 36

DivEqn

.LHS /9.=.RHS /9.

9x/9 = 36/9

CalcQuot

Calculate quotient

x = 4

The solution to the equation is x=4. We can check our solution by substituting it into the original equation.

13x+2 = 4x+38

Substitute

x= 4

13( 4)+2 = 4( 4)+38

Multiply

Multiply

52+2 = 54

AddTerms

Add terms

54 = 54

Since the left-hand side is equal to the right-hand side, our solution is correct.