Pre-Algebra Examples

$\frac{2}{5} \cdot (x - 7) = \frac{3}{4} \cdot (4 x - 3)$

Step 1

Simplify $\frac{2}{5} \cdot (x - 7)$ .

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Step 1.1

Apply the distributive property.

$\frac{2}{5} x + \frac{2}{5} \cdot - 7 = \frac{3}{4} \cdot (4 x - 3)$

Step 1.2

Combine $\frac{2}{5}$ and $x$ .

$\frac{2 x}{5} + \frac{2}{5} \cdot - 7 = \frac{3}{4} \cdot (4 x - 3)$

Step 1.3

Multiply $\frac{2}{5} \cdot - 7$ .

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Step 1.3.1

Combine $\frac{2}{5}$ and $- 7$ .

$\frac{2 x}{5} + \frac{2 \cdot - 7}{5} = \frac{3}{4} \cdot (4 x - 3)$

Step 1.3.2

Multiply $2$ by $- 7$ .

$\frac{2 x}{5} + \frac{- 14}{5} = \frac{3}{4} \cdot (4 x - 3)$

Step 1.4

Move the negative in front of the fraction.

$\frac{2 x}{5} - \frac{14}{5} = \frac{3}{4} \cdot (4 x - 3)$

Step 2

Simplify $\frac{3}{4} \cdot (4 x - 3)$ .

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Step 2.1

Apply the distributive property.

$\frac{2 x}{5} - \frac{14}{5} = \frac{3}{4} (4 x) + \frac{3}{4} \cdot - 3$

Step 2.2

Cancel the common factor of $4$ .

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Step 2.2.1

Factor $4$ out of $4 x$ .

$\frac{2 x}{5} - \frac{14}{5} = \frac{3}{4} (4 (x)) + \frac{3}{4} \cdot - 3$

Step 2.2.2

Cancel the common factor.

$\frac{2 x}{5} - \frac{14}{5} = \frac{3}{4} (4 x) + \frac{3}{4} \cdot - 3$

Step 2.2.3

Rewrite the expression.

$\frac{2 x}{5} - \frac{14}{5} = 3 x + \frac{3}{4} \cdot - 3$

Step 2.3

Multiply $\frac{3}{4} \cdot - 3$ .

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Step 2.3.1

Combine $\frac{3}{4}$ and $- 3$ .

$\frac{2 x}{5} - \frac{14}{5} = 3 x + \frac{3 \cdot - 3}{4}$

Step 2.3.2

Multiply $3$ by $- 3$ .

$\frac{2 x}{5} - \frac{14}{5} = 3 x + \frac{- 9}{4}$

Step 2.4

Move the negative in front of the fraction.

$\frac{2 x}{5} - \frac{14}{5} = 3 x - \frac{9}{4}$

Step 3

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

$x \approx - 0.21153846$

Step 4