Algebra Examples

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

Step 1

Simplify $- 6 x + \frac{1}{2} \cdot (x - 1) - \frac{3}{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Combine $\frac{1}{2}$ and $x$ .

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

Step 1.1.3

Combine $\frac{1}{2}$ and $- 1$ .

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

Step 1.1.4

Move the negative in front of the fraction.

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

Step 1.2

Combine fractions.

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Step 1.2.1

Combine the numerators over the common denominator.

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

Step 1.2.2

Subtract $3$ from $- 1$ .

$- 6 x + \frac{x - 4}{2} = - 3 x$

Step 1.3

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

$- 6 x \cdot \frac{2}{2} + \frac{x - 4}{2} = - 3 x$

Step 1.4

Simplify terms.

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Step 1.4.1

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

$\frac{- 6 x \cdot 2}{2} + \frac{x - 4}{2} = - 3 x$

Step 1.4.2

Combine the numerators over the common denominator.

$\frac{- 6 x \cdot 2 + x - 4}{2} = - 3 x$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $- 6$ .

$\frac{- 12 x + x - 4}{2} = - 3 x$

Step 1.5.2

Add $- 12 x$ and $x$ .

$\frac{- 11 x - 4}{2} = - 3 x$

Step 1.6

Simplify with factoring out.

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Step 1.6.1

Factor $- 1$ out of $- 11 x$ .

$\frac{- (11 x) - 4}{2} = - 3 x$

Step 1.6.2

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- (11 x) - 1 (4)}{2} = - 3 x$

Step 1.6.3

Factor $- 1$ out of $- (11 x) - 1 (4)$ .

$\frac{- (11 x + 4)}{2} = - 3 x$

Step 1.6.4

Simplify the expression.

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Step 1.6.4.1

Rewrite $- (11 x + 4)$ as $- 1 (11 x + 4)$ .

$\frac{- 1 (11 x + 4)}{2} = - 3 x$

Step 1.6.4.2

Move the negative in front of the fraction.

$- \frac{11 x + 4}{2} = - 3 x$

Step 2

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

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Step 2.1

Add $3 x$ to both sides of the equation.

$- \frac{11 x + 4}{2} + 3 x = 0$

Step 2.2

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{11 x + 4}{2} + 3 x \cdot \frac{2}{2} = 0$

Step 2.3

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

$- \frac{11 x + 4}{2} + \frac{3 x \cdot 2}{2} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- (11 x + 4) + 3 x \cdot 2}{2} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Apply the distributive property.

$\frac{- (11 x) - 1 \cdot 4 + 3 x \cdot 2}{2} = 0$

Step 2.5.2

Multiply $11$ by $- 1$ .

$\frac{- 11 x - 1 \cdot 4 + 3 x \cdot 2}{2} = 0$

Step 2.5.3

Multiply $- 1$ by $4$ .

$\frac{- 11 x - 4 + 3 x \cdot 2}{2} = 0$

Step 2.5.4

Multiply $2$ by $3$ .

$\frac{- 11 x - 4 + 6 x}{2} = 0$

Step 2.5.5

Add $- 11 x$ and $6 x$ .

$\frac{- 5 x - 4}{2} = 0$

Step 2.6

Factor $- 1$ out of $- 5 x$ .

$\frac{- (5 x) - 4}{2} = 0$

Step 2.7

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- (5 x) - 1 (4)}{2} = 0$

Step 2.8

Factor $- 1$ out of $- (5 x) - 1 (4)$ .

$\frac{- (5 x + 4)}{2} = 0$

Step 2.9

Rewrite $- (5 x + 4)$ as $- 1 (5 x + 4)$ .

$\frac{- 1 (5 x + 4)}{2} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{5 x + 4}{2} = 0$

Step 3

Set the numerator equal to zero.

$5 x + 4 = 0$

Step 4

Solve the equation for $x$ .

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Step 4.1

Subtract $4$ from both sides of the equation.

$5 x = - 4$

Step 4.2

Divide each term in $5 x = - 4$ by $5$ and simplify.

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Step 4.2.1

Divide each term in $5 x = - 4$ by $5$ .

$\frac{5 x}{5} = \frac{- 4}{5}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $5$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 4}{5}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{5}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$x = - \frac{4}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{5}$

Decimal Form:

$x = - 0.8$