Exercise 40 Page 141

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.

\frac{x - 3}{4} = \frac{x}{2}

CrossMult

Cross multiply

2 (x - 3) = 4 x

DivEqn

$LHS / 2 = RHS / 2$

x - 3 = 2 x

SubEqn

$LHS - x = RHS - x$

- 3 = x

RearrangeEqn

Rearrange equation

x = - 3

The solution to the equation is

x = - 3 .

We can check our solution by substituting it into the original equation.

\frac{x - 3}{4} = \frac{x}{2}

Substitute

$x = - 3$

\frac{- 3 - 3}{4} = ? \frac{- 3}{2}

AddTerms

Add terms

\frac{- 6}{4} = ? \frac{- 3}{2}

ReduceFrac

$\frac{a}{b} = \frac{a / 2}{b / 2}$

\frac{- 3}{2} = \frac{- 3}{2}

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