Algebra Examples

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

Step 1

Rewrite the equation as $3 x - 2 = \frac{11}{2}$ .

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

Step 2

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

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Step 2.1

Add $2$ to both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $2$ .

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

Step 2.5.2

Add $11$ and $4$ .

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

Step 3

Divide each term in $3 x = \frac{15}{2}$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x = \frac{15}{2}$ by $3$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $x$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{15}{2} \cdot \frac{1}{3}$

Step 3.3.2

Cancel the common factor of $3$ .

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Step 3.3.2.1

Factor $3$ out of $15$ .

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

Step 3.3.2.2

Cancel the common factor.

$x = \frac{3 \cdot 5}{2} \cdot \frac{1}{3}$

Step 3.3.2.3

Rewrite the expression.

$x = \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

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