Algebra Examples

$\frac{1}{5} (5 x - 5) + 3 x = - 9 (\frac{1}{3} X + 4)$

Step 1

Simplify $\frac{1}{5} \cdot (5 x - 5) + 3 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{5} (5 x) + \frac{1}{5} \cdot - 5 + 3 x = - 9 (\frac{1}{3} X + 4)$

Step 1.1.2

Cancel the common factor of $5$ .

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Step 1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) + \frac{1}{5} \cdot - 5 + 3 x = - 9 (\frac{1}{3} X + 4)$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 x) + \frac{1}{5} \cdot - 5 + 3 x = - 9 (\frac{1}{3} X + 4)$

Step 1.1.2.3

Rewrite the expression.

$x + \frac{1}{5} \cdot - 5 + 3 x = - 9 (\frac{1}{3} X + 4)$

Step 1.1.3

Cancel the common factor of $5$ .

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Step 1.1.3.1

Factor $5$ out of $- 5$ .

$x + \frac{1}{5} \cdot (5 (- 1)) + 3 x = - 9 (\frac{1}{3} X + 4)$

Step 1.1.3.2

Cancel the common factor.

$x + \frac{1}{5} \cdot (5 \cdot - 1) + 3 x = - 9 (\frac{1}{3} X + 4)$

Step 1.1.3.3

Rewrite the expression.

$x - 1 + 3 x = - 9 (\frac{1}{3} X + 4)$

Step 1.2

Add $x$ and $3 x$ .

$4 x - 1 = - 9 (\frac{1}{3} X + 4)$

Step 2

Simplify $- 9 (\frac{1}{3} X + 4)$ .

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Step 2.1

Combine $\frac{1}{3}$ and $X$ .

$4 x - 1 = - 9 (\frac{X}{3} + 4)$

Step 2.2

Apply the distributive property.

$4 x - 1 = - 9 \frac{X}{3} - 9 \cdot 4$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Factor $3$ out of $- 9$ .

$4 x - 1 = 3 (- 3) \frac{X}{3} - 9 \cdot 4$

Step 2.3.2

Cancel the common factor.

$4 x - 1 = 3 \cdot - 3 \frac{X}{3} - 9 \cdot 4$

Step 2.3.3

Rewrite the expression.

$4 x - 1 = - 3 X - 9 \cdot 4$

Step 2.4

Multiply $- 9$ by $4$ .

$4 x - 1 = - 3 X - 36$

Step 3

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

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Step 3.1

Add $1$ to both sides of the equation.

$4 x = - 3 X - 36 + 1$

Step 3.2

Add $- 36$ and $1$ .

$4 x = - 3 X - 35$

Step 4

Divide each term in $4 x = - 3 X - 35$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 x = - 3 X - 35$ by $4$ .

$\frac{4 x}{4} = \frac{- 3 X}{4} + \frac{- 35}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 3 X}{4} + \frac{- 35}{4}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3 X}{4} + \frac{- 35}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative in front of the fraction.

$x = - \frac{3 X}{4} + \frac{- 35}{4}$

Step 4.3.1.2

Move the negative in front of the fraction.

$x = - \frac{3 X}{4} - \frac{35}{4}$