Pre-Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

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

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

Step 1.3.2

Multiply $5$ by $3$ .

$\frac{2 x \cdot 3}{15} - \frac{x}{3} \cdot \frac{5}{5} = 3$

Step 1.3.3

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

$\frac{2 x \cdot 3}{15} - \frac{x \cdot 5}{3 \cdot 5} = 3$

Step 1.3.4

Multiply $3$ by $5$ .

$\frac{2 x \cdot 3}{15} - \frac{x \cdot 5}{15} = 3$

Step 1.4

Combine the numerators over the common denominator.

$\frac{2 x \cdot 3 - x \cdot 5}{15} = 3$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $x$ out of $2 x \cdot 3 - x \cdot 5$ .

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Step 1.5.1.1

Factor $x$ out of $2 x \cdot 3$ .

$\frac{x (2 \cdot 3) - x \cdot 5}{15} = 3$

Step 1.5.1.2

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (2 \cdot 3) + x (- 1 \cdot 5)}{15} = 3$

Step 1.5.1.3

Factor $x$ out of $x (2 \cdot 3) + x (- 1 \cdot 5)$ .

$\frac{x (2 \cdot 3 - 1 \cdot 5)}{15} = 3$

Step 1.5.2

Multiply $2$ by $3$ .

$\frac{x (6 - 1 \cdot 5)}{15} = 3$

Step 1.5.3

Multiply $- 1$ by $5$ .

$\frac{x (6 - 5)}{15} = 3$

Step 1.5.4

Subtract $5$ from $6$ .

$\frac{x \cdot 1}{15} = 3$

Step 1.6

Multiply $x$ by $1$ .

$\frac{x}{15} = 3$

Step 2

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

$x \approx 45$

Step 3