Pre-Algebra Examples

$\frac{2 x + 22}{4} - \frac{x + 3}{2} = \frac{35}{8}$

Step 1

Simplify $\frac{2 x + 22}{4} - \frac{x + 3}{2}$ .

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Step 1.1

Simplify terms.

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Step 1.1.1

Cancel the common factor of $2 x + 22$ and $4$ .

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Step 1.1.1.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 22}{4} - \frac{x + 3}{2} = \frac{35}{8}$

Step 1.1.1.2

Factor $2$ out of $22$ .

$\frac{2 x + 2 \cdot 11}{4} - \frac{x + 3}{2} = \frac{35}{8}$

Step 1.1.1.3

Factor $2$ out of $2 x + 2 \cdot 11$ .

$\frac{2 (x + 11)}{4} - \frac{x + 3}{2} = \frac{35}{8}$

Step 1.1.1.4

Cancel the common factors.

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Step 1.1.1.4.1

Factor $2$ out of $4$ .

$\frac{2 (x + 11)}{2 (2)} - \frac{x + 3}{2} = \frac{35}{8}$

Step 1.1.1.4.2

Cancel the common factor.

$\frac{2 (x + 11)}{2 \cdot 2} - \frac{x + 3}{2} = \frac{35}{8}$

Step 1.1.1.4.3

Rewrite the expression.

$\frac{x + 11}{2} - \frac{x + 3}{2} = \frac{35}{8}$

Step 1.1.2

Combine the numerators over the common denominator.

$\frac{x + 11 - (x + 3)}{2} = \frac{35}{8}$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\frac{x + 11 - x - 1 \cdot 3}{2} = \frac{35}{8}$

Step 1.2.2

Multiply $- 1$ by $3$ .

$\frac{x + 11 - x - 3}{2} = \frac{35}{8}$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Combine the opposite terms in $x + 11 - x - 3$ .

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Step 1.3.1.1

Subtract $x$ from $x$ .

$\frac{0 + 11 - 3}{2} = \frac{35}{8}$

Step 1.3.1.2

Add $0$ and $11$ .

$\frac{11 - 3}{2} = \frac{35}{8}$

Step 1.3.2

Simplify the expression.

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Step 1.3.2.1

Subtract $3$ from $11$ .

$\frac{8}{2} = \frac{35}{8}$

Step 1.3.2.2

Divide $8$ by $2$ .

$4 = \frac{35}{8}$

Step 2

Since $4 \neq \frac{35}{8}$ , there are no solutions.

No solution