Algebra Examples

$19 + \frac{x + 3}{2} - 14 = 1$

Step 1

Simplify $19 + \frac{x + 3}{2} - 14$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Write $19$ as a fraction with denominator $1$ .

$\frac{19}{1} + \frac{x + 3}{2} - 14 = 1$

Step 1.1.2

Multiply $\frac{19}{1}$ by $\frac{2}{2}$ .

$\frac{19}{1} \cdot \frac{2}{2} + \frac{x + 3}{2} - 14 = 1$

Step 1.1.3

Multiply $\frac{19}{1}$ by $\frac{2}{2}$ .

$\frac{19 \cdot 2}{2} + \frac{x + 3}{2} - 14 = 1$

Step 1.1.4

Write $- 14$ as a fraction with denominator $1$ .

$\frac{19 \cdot 2}{2} + \frac{x + 3}{2} + \frac{- 14}{1} = 1$

Step 1.1.5

Multiply $\frac{- 14}{1}$ by $\frac{2}{2}$ .

$\frac{19 \cdot 2}{2} + \frac{x + 3}{2} + \frac{- 14}{1} \cdot \frac{2}{2} = 1$

Step 1.1.6

Multiply $\frac{- 14}{1}$ by $\frac{2}{2}$ .

$\frac{19 \cdot 2}{2} + \frac{x + 3}{2} + \frac{- 14 \cdot 2}{2} = 1$

Step 1.2

Combine the numerators over the common denominator.

$\frac{19 \cdot 2 + x + 3 - 14 \cdot 2}{2} = 1$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $19$ by $2$ .

$\frac{38 + x + 3 - 14 \cdot 2}{2} = 1$

Step 1.3.2

Multiply $- 14$ by $2$ .

$\frac{38 + x + 3 - 28}{2} = 1$

Step 1.4

Simplify by adding and subtracting.

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Step 1.4.1

Add $38$ and $3$ .

$\frac{x + 41 - 28}{2} = 1$

Step 1.4.2

Subtract $28$ from $41$ .

$\frac{x + 13}{2} = 1$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{x + 13}{2} = 2 \cdot 1$

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 $2$ .

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Step 3.1.1.1

Cancel the common factor.

$2 \frac{x + 13}{2} = 2 \cdot 1$

Step 3.1.1.2

Rewrite the expression.

$x + 13 = 2 \cdot 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $1$ .

$x + 13 = 2$

Step 4

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

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Step 4.1

Subtract $13$ from both sides of the equation.

$x = 2 - 13$

Step 4.2

Subtract $13$ from $2$ .

$x = - 11$