Algebra Examples

$\frac{1}{7} + \frac{2 x}{3} = \frac{15 x - 3}{21}$

Step 1

Cancel the common factor of $15 x - 3$ and $21$ .

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Step 1.1

Factor $3$ out of $15 x$ .

$\frac{1}{7} + \frac{2 x}{3} = \frac{3 (5 x) - 3}{21}$

Step 1.2

Factor $3$ out of $- 3$ .

$\frac{1}{7} + \frac{2 x}{3} = \frac{3 (5 x) + 3 (- 1)}{21}$

Step 1.3

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

$\frac{1}{7} + \frac{2 x}{3} = \frac{3 (5 x - 1)}{21}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $21$ .

$\frac{1}{7} + \frac{2 x}{3} = \frac{3 (5 x - 1)}{3 (7)}$

Step 1.4.2

Cancel the common factor.

$\frac{1}{7} + \frac{2 x}{3} = \frac{3 (5 x - 1)}{3 \cdot 7}$

Step 1.4.3

Rewrite the expression.

$\frac{1}{7} + \frac{2 x}{3} = \frac{5 x - 1}{7}$

Step 2

Multiply both sides by $7$ .

$(\frac{1}{7} + \frac{2 x}{3}) \cdot 7 = \frac{5 x - 1}{7} \cdot 7$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $(\frac{1}{7} + \frac{2 x}{3}) \cdot 7$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{1}{7} \cdot 7 + \frac{2 x}{3} \cdot 7 = \frac{5 x - 1}{7} \cdot 7$

Step 3.1.1.2

Cancel the common factor of $7$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{1}{7} \cdot 7 + \frac{2 x}{3} \cdot 7 = \frac{5 x - 1}{7} \cdot 7$

Step 3.1.1.2.2

Rewrite the expression.

$1 + \frac{2 x}{3} \cdot 7 = \frac{5 x - 1}{7} \cdot 7$

Step 3.1.1.3

Multiply $\frac{2 x}{3} \cdot 7$ .

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Step 3.1.1.3.1

Combine $\frac{2 x}{3}$ and $7$ .

$1 + \frac{2 x \cdot 7}{3} = \frac{5 x - 1}{7} \cdot 7$

Step 3.1.1.3.2

Multiply $7$ by $2$ .

$1 + \frac{14 x}{3} = \frac{5 x - 1}{7} \cdot 7$

Step 3.1.1.4

Reorder $1$ and $\frac{14 x}{3}$ .

$\frac{14 x}{3} + 1 = \frac{5 x - 1}{7} \cdot 7$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{14 x}{3} + 1 = \frac{5 x - 1}{7} \cdot 7$

Step 3.2.1.2

Rewrite the expression.

$\frac{14 x}{3} + 1 = 5 x - 1$

Step 4

Solve for $x$ .

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Step 4.1

Move all terms containing $x$ to the left side of the equation.

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Step 4.1.1

Subtract $5 x$ from both sides of the equation.

$\frac{14 x}{3} + 1 - 5 x = - 1$

Step 4.1.2

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

$\frac{14 x}{3} - 5 x \cdot \frac{3}{3} + 1 = - 1$

Step 4.1.3

Combine $- 5 x$ and $\frac{3}{3}$ .

$\frac{14 x}{3} + \frac{- 5 x \cdot 3}{3} + 1 = - 1$

Step 4.1.4

Combine the numerators over the common denominator.

$\frac{14 x - 5 x \cdot 3}{3} + 1 = - 1$

Step 4.1.5

Simplify each term.

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Step 4.1.5.1

Simplify the numerator.

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Step 4.1.5.1.1

Factor $x$ out of $14 x - 5 x \cdot 3$ .

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Step 4.1.5.1.1.1

Factor $x$ out of $14 x$ .

$\frac{x \cdot 14 - 5 x \cdot 3}{3} + 1 = - 1$

Step 4.1.5.1.1.2

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

$\frac{x \cdot 14 + x (- 5 \cdot 3)}{3} + 1 = - 1$

Step 4.1.5.1.1.3

Factor $x$ out of $x \cdot 14 + x (- 5 \cdot 3)$ .

$\frac{x (14 - 5 \cdot 3)}{3} + 1 = - 1$

Step 4.1.5.1.2

Multiply $- 5$ by $3$ .

$\frac{x (14 - 15)}{3} + 1 = - 1$

Step 4.1.5.1.3

Subtract $15$ from $14$ .

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

Step 4.1.5.2

Move $- 1$ to the left of $x$ .

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

Step 4.1.5.3

Move the negative in front of the fraction.

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

Step 4.2

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

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Step 4.2.1

Subtract $1$ from both sides of the equation.

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

Step 4.2.2

Subtract $1$ from $- 1$ .

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

Step 4.3

Multiply both sides of the equation by $- 3$ .

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

Step 4.4

Simplify both sides of the equation.

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Step 4.4.1

Simplify the left side.

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Step 4.4.1.1

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

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Step 4.4.1.1.1

Cancel the common factor of $3$ .

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Step 4.4.1.1.1.1

Move the leading negative in $- \frac{x}{3}$ into the numerator.

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

Step 4.4.1.1.1.2

Factor $3$ out of $- 3$ .

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

Step 4.4.1.1.1.3

Cancel the common factor.

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

Step 4.4.1.1.1.4

Rewrite the expression.

$- - x = - 3 \cdot - 2$

Step 4.4.1.1.2

Multiply.

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Step 4.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 3 \cdot - 2$

Step 4.4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 3 \cdot - 2$

Step 4.4.2

Simplify the right side.

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Step 4.4.2.1

Multiply $- 3$ by $- 2$ .

$x = 6$