Algebra Examples

$- 4 x + 24 = 8 - \frac{2}{5} (10 x - 60)$

Step 1

Simplify $8 - \frac{2}{5} \cdot (10 x - 60)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 4 x + 24 = 8 - \frac{2}{5} (10 x) - \frac{2}{5} \cdot - 60$

Step 1.1.2

Cancel the common factor of $5$ .

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Step 1.1.2.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$- 4 x + 24 = 8 + \frac{- 2}{5} (10 x) - \frac{2}{5} \cdot - 60$

Step 1.1.2.2

Factor $5$ out of $10 x$ .

$- 4 x + 24 = 8 + \frac{- 2}{5} (5 (2 x)) - \frac{2}{5} \cdot - 60$

Step 1.1.2.3

Cancel the common factor.

$- 4 x + 24 = 8 + \frac{- 2}{5} (5 (2 x)) - \frac{2}{5} \cdot - 60$

Step 1.1.2.4

Rewrite the expression.

$- 4 x + 24 = 8 - 2 (2 x) - \frac{2}{5} \cdot - 60$

Step 1.1.3

Multiply $2$ by $- 2$ .

$- 4 x + 24 = 8 - 4 x - \frac{2}{5} \cdot - 60$

Step 1.1.4

Cancel the common factor of $5$ .

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Step 1.1.4.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$- 4 x + 24 = 8 - 4 x + \frac{- 2}{5} \cdot - 60$

Step 1.1.4.2

Factor $5$ out of $- 60$ .

$- 4 x + 24 = 8 - 4 x + \frac{- 2}{5} \cdot (5 (- 12))$

Step 1.1.4.3

Cancel the common factor.

$- 4 x + 24 = 8 - 4 x + \frac{- 2}{5} \cdot (5 \cdot - 12)$

Step 1.1.4.4

Rewrite the expression.

$- 4 x + 24 = 8 - 4 x - 2 \cdot - 12$

Step 1.1.5

Multiply $- 2$ by $- 12$ .

$- 4 x + 24 = 8 - 4 x + 24$

Step 1.2

Add $8$ and $24$ .

$- 4 x + 24 = - 4 x + 32$

Step 2

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

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Step 2.1

Add $4 x$ to both sides of the equation.

$- 4 x + 24 + 4 x = 32$

Step 2.2

Combine the opposite terms in $- 4 x + 24 + 4 x$ .

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Step 2.2.1

Add $- 4 x$ and $4 x$ .

$0 + 24 = 32$

Step 2.2.2

Add $0$ and $24$ .

$24 = 32$

Step 3

Since $24 \neq 32$ , there are no solutions.

No solution