Algebra Examples

$4 (3 - 5 x) = 15 - (8 x - 25)$

Step 1

Simplify $4 (3 - 5 x)$ .

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Step 1.1

Rewrite.

$0 + 0 + 4 (3 - 5 x) = 15 - (8 x - 25)$

Step 1.2

Simplify by adding zeros.

$4 (3 - 5 x) = 15 - (8 x - 25)$

Step 1.3

Apply the distributive property.

$4 \cdot 3 + 4 (- 5 x) = 15 - (8 x - 25)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $4$ by $3$ .

$12 + 4 (- 5 x) = 15 - (8 x - 25)$

Step 1.4.2

Multiply $- 5$ by $4$ .

$12 - 20 x = 15 - (8 x - 25)$

$12 - 20 x = 15 - (8 x - 25)$

$12 - 20 x = 15 - (8 x - 25)$

Step 2

Simplify $15 - (8 x - 25)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$12 - 20 x = 15 - (8 x) - - 25$

Step 2.1.2

Multiply $8$ by $- 1$ .

$12 - 20 x = 15 - 8 x - - 25$

Step 2.1.3

Multiply $- 1$ by $- 25$ .

$12 - 20 x = 15 - 8 x + 25$

$12 - 20 x = 15 - 8 x + 25$

Step 2.2

Add $15$ and $25$ .

$12 - 20 x = - 8 x + 40$

$12 - 20 x = - 8 x + 40$

Step 3

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

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Step 3.1

Add $8 x$ to both sides of the equation.

$12 - 20 x + 8 x = 40$

Step 3.2

Add $- 20 x$ and $8 x$ .

$12 - 12 x = 40$

$12 - 12 x = 40$

Step 4

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

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Step 4.1

Subtract $12$ from both sides of the equation.

$- 12 x = 40 - 12$

Step 4.2

Subtract $12$ from $40$ .

$- 12 x = 28$

$- 12 x = 28$

Step 5

Divide each term in $- 12 x = 28$ by $- 12$ and simplify.

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Step 5.1

Divide each term in $- 12 x = 28$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{28}{- 12}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 12$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{28}{- 12}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{28}{- 12}$

$x = \frac{28}{- 12}$

$x = \frac{28}{- 12}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $28$ and $- 12$ .

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Step 5.3.1.1

Factor $4$ out of $28$ .

$x = \frac{4 (7)}{- 12}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $4$ out of $- 12$ .

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

Step 5.3.1.2.2

Cancel the common factor.

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

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{7}{- 3}$

$x = \frac{7}{- 3}$

$x = \frac{7}{- 3}$

Step 5.3.2

Move the negative in front of the fraction.

$x = - \frac{7}{3}$

$x = - \frac{7}{3}$

$x = - \frac{7}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{3}$

Decimal Form:

$x = - 2.\overline{3}$

Mixed Number Form:

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$