Algebra Examples

$4 - \frac{5}{2} = \frac{x + 7}{18}$

Step 1

Rewrite the equation as $\frac{x + 7}{18} = 4 - \frac{5}{2}$ .

$\frac{x + 7}{18} = 4 - \frac{5}{2}$

Step 2

Multiply both sides of the equation by $18$ .

$18 \frac{x + 7}{18} = 18 (4 - \frac{5}{2})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $18$ .

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Step 3.1.1.1

Cancel the common factor.

$18 \frac{x + 7}{18} = 18 (4 - \frac{5}{2})$

Step 3.1.1.2

Rewrite the expression.

$x + 7 = 18 (4 - \frac{5}{2})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $18 (4 - \frac{5}{2})$ .

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Step 3.2.1.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x + 7 = 18 (4 \cdot \frac{2}{2} - \frac{5}{2})$

Step 3.2.1.2

Combine $4$ and $\frac{2}{2}$ .

$x + 7 = 18 (\frac{4 \cdot 2}{2} - \frac{5}{2})$

Step 3.2.1.3

Combine the numerators over the common denominator.

$x + 7 = 18 \frac{4 \cdot 2 - 5}{2}$

Step 3.2.1.4

Simplify the numerator.

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Step 3.2.1.4.1

Multiply $4$ by $2$ .

$x + 7 = 18 \frac{8 - 5}{2}$

Step 3.2.1.4.2

Subtract $5$ from $8$ .

$x + 7 = 18 (\frac{3}{2})$

Step 3.2.1.5

Cancel the common factor of $2$ .

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Step 3.2.1.5.1

Factor $2$ out of $18$ .

$x + 7 = 2 (9) \frac{3}{2}$

Step 3.2.1.5.2

Cancel the common factor.

$x + 7 = 2 \cdot 9 \frac{3}{2}$

Step 3.2.1.5.3

Rewrite the expression.

$x + 7 = 9 \cdot 3$

Step 3.2.1.6

Multiply $9$ by $3$ .

$x + 7 = 27$

Step 4

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

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Step 4.1

Subtract $7$ from both sides of the equation.

$x = 27 - 7$

Step 4.2

Subtract $7$ from $27$ .

$x = 20$