Algebra Examples

$x - 3 = \frac{5}{2} x - 4$

Step 1

Combine $\frac{5}{2}$ and $x$ .

$x - 3 = \frac{5 x}{2} - 4$

Step 2

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

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Step 2.1

Subtract $\frac{5 x}{2}$ from both sides of the equation.

$x - 3 - \frac{5 x}{2} = - 4$

Step 2.2

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

$x \cdot \frac{2}{2} - \frac{5 x}{2} - 3 = - 4$

Step 2.3

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

$\frac{x \cdot 2}{2} - \frac{5 x}{2} - 3 = - 4$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 - 5 x}{2} - 3 = - 4$

Step 2.5

Subtract $5 x$ from $x \cdot 2$ .

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Step 2.5.1

Reorder $x$ and $2$ .

$\frac{2 \cdot x - 5 x}{2} - 3 = - 4$

Step 2.5.2

Subtract $5 x$ from $2 \cdot x$ .

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

Step 2.6

Move the negative in front of the fraction.

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

Step 3

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

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Step 3.1

Add $3$ to both sides of the equation.

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

Step 3.2

Add $- 4$ and $3$ .

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

Step 4

Multiply both sides of the equation by $- \frac{2}{3}$ .

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

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{2}{3} (- \frac{3 x}{2})$ .

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 5.1.1.1.2

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

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

Step 5.1.1.1.3

Factor $2$ out of $- 2$ .

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

Step 5.1.1.1.4

Cancel the common factor.

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

Step 5.1.1.1.5

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

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

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

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

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 5.1.1.3.2

Multiply $x$ by $1$ .

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

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- \frac{2}{3} \cdot - 1$ .

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Step 5.2.1.1

Multiply $- 1$ by $- 1$ .

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

Step 5.2.1.2

Multiply $\frac{2}{3}$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{6}$