Algebra Examples

$\frac{3}{2} - \frac{3}{2} x = 6 (- 4 x - 1) + 9 x$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$6 (- 4 x - 1) + 9 x = \frac{3}{2} - \frac{3}{2} x$

Step 2

Simplify $6 (- 4 x - 1) + 9 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$6 (- 4 x) + 6 \cdot - 1 + 9 x = \frac{3}{2} - \frac{3}{2} x$

Step 2.1.2

Multiply $- 4$ by $6$ .

$- 24 x + 6 \cdot - 1 + 9 x = \frac{3}{2} - \frac{3}{2} x$

Step 2.1.3

Multiply $6$ by $- 1$ .

$- 24 x - 6 + 9 x = \frac{3}{2} - \frac{3}{2} x$

Step 2.2

Add $- 24 x$ and $9 x$ .

$- 15 x - 6 = \frac{3}{2} - \frac{3}{2} x$

Step 3

Simplify each term.

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Step 3.1

Combine $x$ and $\frac{3}{2}$ .

$- 15 x - 6 = \frac{3}{2} - \frac{x \cdot 3}{2}$

Step 3.2

Move $3$ to the left of $x$ .

$- 15 x - 6 = \frac{3}{2} - \frac{3 x}{2}$

Step 4

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

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Step 4.1

Add $\frac{3 x}{2}$ to both sides of the equation.

$- 15 x - 6 + \frac{3 x}{2} = \frac{3}{2}$

Step 4.2

To write $- 15 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 15 x \cdot \frac{2}{2} + \frac{3 x}{2} - 6 = \frac{3}{2}$

Step 4.3

Combine $- 15 x$ and $\frac{2}{2}$ .

$\frac{- 15 x \cdot 2}{2} + \frac{3 x}{2} - 6 = \frac{3}{2}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{- 15 x \cdot 2 + 3 x}{2} - 6 = \frac{3}{2}$

Step 4.5

Simplify each term.

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Step 4.5.1

Simplify the numerator.

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Step 4.5.1.1

Factor $3 x$ out of $- 15 x \cdot 2 + 3 x$ .

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Step 4.5.1.1.1

Factor $3 x$ out of $- 15 x \cdot 2$ .

$\frac{3 x (- 5 \cdot 2) + 3 x}{2} - 6 = \frac{3}{2}$

Step 4.5.1.1.2

Factor $3 x$ out of $3 x$ .

$\frac{3 x (- 5 \cdot 2) + 3 x (1)}{2} - 6 = \frac{3}{2}$

Step 4.5.1.1.3

Factor $3 x$ out of $3 x (- 5 \cdot 2) + 3 x (1)$ .

$\frac{3 x (- 5 \cdot 2 + 1)}{2} - 6 = \frac{3}{2}$

Step 4.5.1.2

Multiply $- 5$ by $2$ .

$\frac{3 x (- 10 + 1)}{2} - 6 = \frac{3}{2}$

Step 4.5.1.3

Add $- 10$ and $1$ .

$\frac{3 x \cdot - 9}{2} - 6 = \frac{3}{2}$

Step 4.5.1.4

Multiply $- 9$ by $3$ .

$\frac{- 27 x}{2} - 6 = \frac{3}{2}$

Step 4.5.2

Move the negative in front of the fraction.

$- \frac{27 x}{2} - 6 = \frac{3}{2}$

Step 5

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

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Step 5.1

Add $6$ to both sides of the equation.

$- \frac{27 x}{2} = \frac{3}{2} + 6$

Step 5.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{27 x}{2} = \frac{3}{2} + 6 \cdot \frac{2}{2}$

Step 5.3

Combine $6$ and $\frac{2}{2}$ .

$- \frac{27 x}{2} = \frac{3}{2} + \frac{6 \cdot 2}{2}$

Step 5.4

Combine the numerators over the common denominator.

$- \frac{27 x}{2} = \frac{3 + 6 \cdot 2}{2}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $6$ by $2$ .

$- \frac{27 x}{2} = \frac{3 + 12}{2}$

Step 5.5.2

Add $3$ and $12$ .

$- \frac{27 x}{2} = \frac{15}{2}$

Step 6

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 27 x = 15$

Step 7

Divide each term in $- 27 x = 15$ by $- 27$ and simplify.

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Step 7.1

Divide each term in $- 27 x = 15$ by $- 27$ .

$\frac{- 27 x}{- 27} = \frac{15}{- 27}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $- 27$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{- 27 x}{- 27} = \frac{15}{- 27}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{- 27}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Cancel the common factor of $15$ and $- 27$ .

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Step 7.3.1.1

Factor $3$ out of $15$ .

$x = \frac{3 (5)}{- 27}$

Step 7.3.1.2

Cancel the common factors.

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Step 7.3.1.2.1

Factor $3$ out of $- 27$ .

$x = \frac{3 \cdot 5}{3 \cdot - 9}$

Step 7.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 5}{3 \cdot - 9}$

Step 7.3.1.2.3

Rewrite the expression.

$x = \frac{5}{- 9}$

Step 7.3.2

Move the negative in front of the fraction.

$x = - \frac{5}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5}{9}$

Decimal Form:

$x = - 0.\overline{5}$