Algebra Examples

$- 5 (1 - 5 x) + 5 (- 8 x - 2) = - 4 x - 8 x$

Step 1

Simplify $- 5 (1 - 5 x) + 5 (- 8 x - 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 5 \cdot 1 - 5 (- 5 x) + 5 (- 8 x - 2) = - 4 x - 8 x$

Step 1.1.2

Multiply $- 5$ by $1$ .

$- 5 - 5 (- 5 x) + 5 (- 8 x - 2) = - 4 x - 8 x$

Step 1.1.3

Multiply $- 5$ by $- 5$ .

$- 5 + 25 x + 5 (- 8 x - 2) = - 4 x - 8 x$

Step 1.1.4

Apply the distributive property.

$- 5 + 25 x + 5 (- 8 x) + 5 \cdot - 2 = - 4 x - 8 x$

Step 1.1.5

Multiply $- 8$ by $5$ .

$- 5 + 25 x - 40 x + 5 \cdot - 2 = - 4 x - 8 x$

Step 1.1.6

Multiply $5$ by $- 2$ .

$- 5 + 25 x - 40 x - 10 = - 4 x - 8 x$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $10$ from $- 5$ .

$25 x - 40 x - 15 = - 4 x - 8 x$

Step 1.2.2

Subtract $40 x$ from $25 x$ .

$- 15 x - 15 = - 4 x - 8 x$

Step 2

Subtract $8 x$ from $- 4 x$ .

$- 15 x - 15 = - 12 x$

Step 3

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

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Step 3.1

Add $12 x$ to both sides of the equation.

$- 15 x - 15 + 12 x = 0$

Step 3.2

Add $- 15 x$ and $12 x$ .

$- 3 x - 15 = 0$

Step 4

Add $15$ to both sides of the equation.

$- 3 x = 15$

Step 5

Divide each term in $- 3 x = 15$ by $- 3$ and simplify.

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Step 5.1

Divide each term in $- 3 x = 15$ by $- 3$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 3$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $15$ by $- 3$ .

$x = - 5$