Algebra Examples

$\frac{4 x}{5} - 3 = 1 + \frac{x}{5} + x - 8$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$1 + \frac{x}{5} + x - 8 = \frac{4 x}{5} - 3$

Step 2

Simplify $1 + \frac{x}{5} + x - 8$ .

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Step 2.1

Subtract $8$ from $1$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Add $x$ and $x \cdot 5$ .

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Step 2.5.1

Reorder $x$ and $5$ .

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

Step 2.5.2

Add $x$ and $5 \cdot x$ .

$\frac{6 x}{5} - 7 = \frac{4 x}{5} - 3$

Step 3

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

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Step 3.1

Subtract $\frac{4 x}{5}$ from both sides of the equation.

$\frac{6 x}{5} - 7 - \frac{4 x}{5} = - 3$

Step 3.2

Combine the numerators over the common denominator.

$- 7 + \frac{6 x - 4 x}{5} = - 3$

Step 3.3

Subtract $4 x$ from $6 x$ .

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

Step 4

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

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Step 4.1

Add $7$ to both sides of the equation.

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

Step 4.2

Add $- 3$ and $7$ .

$\frac{2 x}{5} = 4$

Step 5

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{2 x}{5} = \frac{5}{2} \cdot 4$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{5}{2} \cdot \frac{2 x}{5}$ .

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Step 6.1.1.1

Cancel the common factor of $5$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 x}{5} = \frac{5}{2} \cdot 4$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{5}{2} \cdot 4$

Step 6.1.1.2

Cancel the common factor of $2$ .

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Step 6.1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{5}{2} \cdot 4$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{5}{2} \cdot 4$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{5}{2} \cdot 4$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{5}{2} \cdot 4$ .

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Factor $2$ out of $4$ .

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

Step 6.2.1.1.2

Cancel the common factor.

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

Step 6.2.1.1.3

Rewrite the expression.

$x = 5 \cdot 2$

Step 6.2.1.2

Multiply $5$ by $2$ .

$x = 10$