Solve for x -1 1/2=3x-4 1/2

$- 1 \frac{1}{2} = 3 x - 4 \frac{1}{2}$

Step 1

Simplify the left side.

Convert $1 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- (1 + \frac{1}{2}) = 3 x - 4 \frac{1}{2}$

Add $1$ and $\frac{1}{2}$ .

Write $1$ as a fraction with a common denominator.

$- (\frac{2}{2} + \frac{1}{2}) = 3 x - 4 \frac{1}{2}$

Combine the numerators over the common denominator.

$- \frac{2 + 1}{2} = 3 x - 4 \frac{1}{2}$

Add $2$ and $1$ .

$- \frac{3}{2} = 3 x - 4 \frac{1}{2}$

Step 2

Simplify the right side.

Convert $4 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- \frac{3}{2} = 3 x - (4 + \frac{1}{2})$

Add $4$ and $\frac{1}{2}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3}{2} = 3 x - (4 \cdot \frac{2}{2} + \frac{1}{2})$

Combine $4$ and $\frac{2}{2}$ .

$- \frac{3}{2} = 3 x - (\frac{4 \cdot 2}{2} + \frac{1}{2})$

Combine the numerators over the common denominator.

$- \frac{3}{2} = 3 x - \frac{4 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $4$ by $2$ .

$- \frac{3}{2} = 3 x - \frac{8 + 1}{2}$

Add $8$ and $1$ .

$- \frac{3}{2} = 3 x - \frac{9}{2}$

Step 3

Rewrite the equation as $3 x - \frac{9}{2} = - \frac{3}{2}$ .

$3 x - \frac{9}{2} = - \frac{3}{2}$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Add $\frac{9}{2}$ to both sides of the equation.

$3 x = - \frac{3}{2} + \frac{9}{2}$

Combine the numerators over the common denominator.

$3 x = \frac{- 3 + 9}{2}$

Add $- 3$ and $9$ .

$3 x = \frac{6}{2}$

Divide $6$ by $2$ .

$3 x = 3$

Step 5

Divide each term in $3 x = 3$ by $3$ and simplify.

Divide each term in $3 x = 3$ by $3$ .

$\frac{3 x}{3} = \frac{3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{3}{3}$

Divide $x$ by $1$ .

$x = \frac{3}{3}$

Simplify the right side.

Divide $3$ by $3$ .

$x = 1$

Solve for x -1 1/2=3x-4 1/2

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