Algebra Examples

$\frac{1}{5} (10 x - 20) = x - 3$

Step 1

Simplify $\frac{1}{5} \cdot (10 x - 20)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{5} \cdot (10 x - 20) = x - 3$

Step 1.2

Simplify by adding zeros.

$\frac{1}{5} \cdot (10 x - 20) = x - 3$

Step 1.3

Apply the distributive property.

$\frac{1}{5} (10 x) + \frac{1}{5} \cdot - 20 = x - 3$

Step 1.4

Cancel the common factor of $5$ .

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Step 1.4.1

Factor $5$ out of $10 x$ .

$\frac{1}{5} (5 (2 x)) + \frac{1}{5} \cdot - 20 = x - 3$

Step 1.4.2

Cancel the common factor.

$\frac{1}{5} (5 (2 x)) + \frac{1}{5} \cdot - 20 = x - 3$

Step 1.4.3

Rewrite the expression.

$2 x + \frac{1}{5} \cdot - 20 = x - 3$

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Factor $5$ out of $- 20$ .

$2 x + \frac{1}{5} \cdot (5 (- 4)) = x - 3$

Step 1.5.2

Cancel the common factor.

$2 x + \frac{1}{5} \cdot (5 \cdot - 4) = x - 3$

Step 1.5.3

Rewrite the expression.

$2 x - 4 = x - 3$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$2 x - 4 - x = - 3$

Step 2.2

Subtract $x$ from $2 x$ .

$x - 4 = - 3$

Step 3

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

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Step 3.1

Add $4$ to both sides of the equation.

$x = - 3 + 4$

Step 3.2

Add $- 3$ and $4$ .

$x = 1$