Algebra Examples

$3 - 5 (x + 4) = 8 (2 x - 3)$

Step 1

Simplify $3 - 5 (x + 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 - 5 x - 5 \cdot 4 = 8 (2 x - 3)$

Step 1.1.2

Multiply $- 5$ by $4$ .

$3 - 5 x - 20 = 8 (2 x - 3)$

$3 - 5 x - 20 = 8 (2 x - 3)$

Step 1.2

Subtract $20$ from $3$ .

$- 5 x - 17 = 8 (2 x - 3)$

$- 5 x - 17 = 8 (2 x - 3)$

Step 2

Simplify $8 (2 x - 3)$ .

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Step 2.1

Apply the distributive property.

$- 5 x - 17 = 8 (2 x) + 8 \cdot - 3$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $2$ by $8$ .

$- 5 x - 17 = 16 x + 8 \cdot - 3$

Step 2.2.2

Multiply $8$ by $- 3$ .

$- 5 x - 17 = 16 x - 24$

$- 5 x - 17 = 16 x - 24$

$- 5 x - 17 = 16 x - 24$

Step 3

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

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Step 3.1

Subtract $16 x$ from both sides of the equation.

$- 5 x - 17 - 16 x = - 24$

Step 3.2

Subtract $16 x$ from $- 5 x$ .

$- 21 x - 17 = - 24$

$- 21 x - 17 = - 24$

Step 4

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

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Step 4.1

Add $17$ to both sides of the equation.

$- 21 x = - 24 + 17$

Step 4.2

Add $- 24$ and $17$ .

$- 21 x = - 7$

$- 21 x = - 7$

Step 5

Divide each term in $- 21 x = - 7$ by $- 21$ and simplify.

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Step 5.1

Divide each term in $- 21 x = - 7$ by $- 21$ .

$\frac{- 21 x}{- 21} = \frac{- 7}{- 21}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 21$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 21 x}{- 21} = \frac{- 7}{- 21}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{- 21}$

$x = \frac{- 7}{- 21}$

$x = \frac{- 7}{- 21}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 7$ and $- 21$ .

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Step 5.3.1.1

Factor $- 7$ out of $- 7$ .

$x = \frac{- 7 (1)}{- 21}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $- 7$ out of $- 21$ .

$x = \frac{- 7 \cdot 1}{- 7 \cdot 3}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{- 7 \cdot 1}{- 7 \cdot 3}$

Step 5.3.1.2.3

Rewrite the expression.

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

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

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

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{3}$

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