Pre-Algebra Examples

$\frac{1}{4} x - \frac{4}{5} + \frac{3}{2} = \frac{5}{4} x - \frac{2}{3}$

Step 1

Simplify $\frac{1}{4} x - \frac{4}{5} + \frac{3}{2}$ .

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Step 1.1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} - \frac{4}{5} + \frac{3}{2} = \frac{5}{4} x - \frac{2}{3}$

Step 1.2

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{4} - \frac{4}{5} \cdot \frac{2}{2} + \frac{3}{2} = \frac{5}{4} x - \frac{2}{3}$

Step 1.3

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{4} - \frac{4}{5} \cdot \frac{2}{2} + \frac{3}{2} \cdot \frac{5}{5} = \frac{5}{4} x - \frac{2}{3}$

Step 1.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{4}{5}$ by $\frac{2}{2}$ .

$\frac{x}{4} - \frac{4 \cdot 2}{5 \cdot 2} + \frac{3}{2} \cdot \frac{5}{5} = \frac{5}{4} x - \frac{2}{3}$

Step 1.4.2

Multiply $5$ by $2$ .

$\frac{x}{4} - \frac{4 \cdot 2}{10} + \frac{3}{2} \cdot \frac{5}{5} = \frac{5}{4} x - \frac{2}{3}$

Step 1.4.3

Multiply $\frac{3}{2}$ by $\frac{5}{5}$ .

$\frac{x}{4} - \frac{4 \cdot 2}{10} + \frac{3 \cdot 5}{2 \cdot 5} = \frac{5}{4} x - \frac{2}{3}$

Step 1.4.4

Multiply $2$ by $5$ .

$\frac{x}{4} - \frac{4 \cdot 2}{10} + \frac{3 \cdot 5}{10} = \frac{5}{4} x - \frac{2}{3}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{x}{4} + \frac{- 4 \cdot 2 + 3 \cdot 5}{10} = \frac{5}{4} x - \frac{2}{3}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 4$ by $2$ .

$\frac{x}{4} + \frac{- 8 + 3 \cdot 5}{10} = \frac{5}{4} x - \frac{2}{3}$

Step 1.6.2

Multiply $3$ by $5$ .

$\frac{x}{4} + \frac{- 8 + 15}{10} = \frac{5}{4} x - \frac{2}{3}$

Step 1.6.3

Add $- 8$ and $15$ .

$\frac{x}{4} + \frac{7}{10} = \frac{5}{4} x - \frac{2}{3}$

Step 2

Combine $\frac{5}{4}$ and $x$ .

$\frac{x}{4} + \frac{7}{10} = \frac{5 x}{4} - \frac{2}{3}$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 1.36666666$

Step 4