Exercise 10 Page 115

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 multiplying the equation by 3.

2/3(x-4)=1/3(2x-6)

MultEqn

LHS * 3=RHS* 3

3*2/3(x-4)=3*1/3(2x-6)

DenomMultFracToNumber

3 * a/3= a

2(x-4)=2x-6

Distr

Distribute 2

2x-8=2x-6

Now, we can continue to solve using the Addition and Division Properties of Equality.

2x-8=2x-6

SubEqn

LHS-2x=RHS-2x

-8≠-6

Simplifying the equation resulted in a contradiction. Thus, the equation has no solution.