Pre-Algebra Examples

$\frac{6 x - 3}{5} + \frac{6}{10} = \frac{12 x + 2}{10}$

Step 1

Simplify $\frac{6 x - 3}{5} + \frac{6}{10}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Factor $3$ out of $6 x - 3$ .

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Step 1.1.1.1

Factor $3$ out of $6 x$ .

$\frac{3 (2 x) - 3}{5} + \frac{6}{10} = \frac{12 x + 2}{10}$

Step 1.1.1.2

Factor $3$ out of $- 3$ .

$\frac{3 (2 x) + 3 (- 1)}{5} + \frac{6}{10} = \frac{12 x + 2}{10}$

Step 1.1.1.3

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

$\frac{3 (2 x - 1)}{5} + \frac{6}{10} = \frac{12 x + 2}{10}$

Step 1.1.2

Cancel the common factor of $6$ and $10$ .

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Step 1.1.2.1

Factor $2$ out of $6$ .

$\frac{3 (2 x - 1)}{5} + \frac{2 (3)}{10} = \frac{12 x + 2}{10}$

Step 1.1.2.2

Cancel the common factors.

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Step 1.1.2.2.1

Factor $2$ out of $10$ .

$\frac{3 (2 x - 1)}{5} + \frac{2 \cdot 3}{2 \cdot 5} = \frac{12 x + 2}{10}$

Step 1.1.2.2.2

Cancel the common factor.

$\frac{3 (2 x - 1)}{5} + \frac{2 \cdot 3}{2 \cdot 5} = \frac{12 x + 2}{10}$

Step 1.1.2.2.3

Rewrite the expression.

$\frac{3 (2 x - 1)}{5} + \frac{3}{5} = \frac{12 x + 2}{10}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{3 (2 x - 1) + 3}{5} = \frac{12 x + 2}{10}$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{3 (2 x) + 3 \cdot - 1 + 3}{5} = \frac{12 x + 2}{10}$

Step 1.3.2

Multiply $2$ by $3$ .

$\frac{6 x + 3 \cdot - 1 + 3}{5} = \frac{12 x + 2}{10}$

Step 1.3.3

Multiply $3$ by $- 1$ .

$\frac{6 x - 3 + 3}{5} = \frac{12 x + 2}{10}$

Step 1.4

Combine the opposite terms in $6 x - 3 + 3$ .

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Step 1.4.1

Add $- 3$ and $3$ .

$\frac{6 x + 0}{5} = \frac{12 x + 2}{10}$

Step 1.4.2

Add $6 x$ and $0$ .

$\frac{6 x}{5} = \frac{12 x + 2}{10}$

Step 2

Cancel the common factor of $12 x + 2$ and $10$ .

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Step 2.1

Factor $2$ out of $12 x$ .

$\frac{6 x}{5} = \frac{2 (6 x) + 2}{10}$

Step 2.2

Factor $2$ out of $2$ .

$\frac{6 x}{5} = \frac{2 (6 x) + 2 (1)}{10}$

Step 2.3

Factor $2$ out of $2 (6 x) + 2 (1)$ .

$\frac{6 x}{5} = \frac{2 (6 x + 1)}{10}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $10$ .

$\frac{6 x}{5} = \frac{2 (6 x + 1)}{2 (5)}$

Step 2.4.2

Cancel the common factor.

$\frac{6 x}{5} = \frac{2 (6 x + 1)}{2 \cdot 5}$

Step 2.4.3

Rewrite the expression.

$\frac{6 x}{5} = \frac{6 x + 1}{5}$

Step 3

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

No solution

Step 4