Algebra Examples

$\frac{5 + 3 x}{10} - \frac{2 (x - 1)}{8} = 1$

Step 1

Simplify $\frac{5 + 3 x}{10} - \frac{2 (x - 1)}{8}$ .

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Step 1.1

Cancel the common factors.

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Step 1.1.1

Factor $2$ out of $8$ .

$\frac{5 + 3 x}{10} - \frac{2 (x - 1)}{2 \cdot 4} = 1$

Step 1.1.2

Cancel the common factor.

$\frac{5 + 3 x}{10} - \frac{2 (x - 1)}{2 \cdot 4} = 1$

Step 1.1.3

Rewrite the expression.

$\frac{5 + 3 x}{10} - \frac{x - 1}{4} = 1$

Step 1.2

To write $\frac{5 + 3 x}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 + 3 x}{10} \cdot \frac{2}{2} - \frac{x - 1}{4} = 1$

Step 1.3

To write $- \frac{x - 1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 + 3 x}{10} \cdot \frac{2}{2} - \frac{x - 1}{4} \cdot \frac{5}{5} = 1$

Step 1.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{5 + 3 x}{10}$ by $\frac{2}{2}$ .

$\frac{(5 + 3 x) \cdot 2}{10 \cdot 2} - \frac{x - 1}{4} \cdot \frac{5}{5} = 1$

Step 1.4.2

Multiply $10$ by $2$ .

$\frac{(5 + 3 x) \cdot 2}{20} - \frac{x - 1}{4} \cdot \frac{5}{5} = 1$

Step 1.4.3

Multiply $\frac{x - 1}{4}$ by $\frac{5}{5}$ .

$\frac{(5 + 3 x) \cdot 2}{20} - \frac{(x - 1) \cdot 5}{4 \cdot 5} = 1$

Step 1.4.4

Multiply $4$ by $5$ .

$\frac{(5 + 3 x) \cdot 2}{20} - \frac{(x - 1) \cdot 5}{20} = 1$

Step 1.5

Combine the numerators over the common denominator.

$\frac{(5 + 3 x) \cdot 2 - (x - 1) \cdot 5}{20} = 1$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Apply the distributive property.

$\frac{5 \cdot 2 + 3 x \cdot 2 - (x - 1) \cdot 5}{20} = 1$

Step 1.6.2

Multiply $5$ by $2$ .

$\frac{10 + 3 x \cdot 2 - (x - 1) \cdot 5}{20} = 1$

Step 1.6.3

Multiply $2$ by $3$ .

$\frac{10 + 6 x - (x - 1) \cdot 5}{20} = 1$

Step 1.6.4

Apply the distributive property.

$\frac{10 + 6 x + (- x - - 1) \cdot 5}{20} = 1$

Step 1.6.5

Multiply $- 1$ by $- 1$ .

$\frac{10 + 6 x + (- x + 1) \cdot 5}{20} = 1$

Step 1.6.6

Apply the distributive property.

$\frac{10 + 6 x - x \cdot 5 + 1 \cdot 5}{20} = 1$

Step 1.6.7

Multiply $5$ by $- 1$ .

$\frac{10 + 6 x - 5 x + 1 \cdot 5}{20} = 1$

Step 1.6.8

Multiply $5$ by $1$ .

$\frac{10 + 6 x - 5 x + 5}{20} = 1$

Step 1.6.9

Add $10$ and $5$ .

$\frac{6 x - 5 x + 15}{20} = 1$

Step 1.6.10

Subtract $5 x$ from $6 x$ .

$\frac{x + 15}{20} = 1$

Step 2

Multiply both sides of the equation by $20$ .

$20 \frac{x + 15}{20} = 20 \cdot 1$

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 $20$ .

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Step 3.1.1.1

Cancel the common factor.

$20 \frac{x + 15}{20} = 20 \cdot 1$

Step 3.1.1.2

Rewrite the expression.

$x + 15 = 20 \cdot 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $20$ by $1$ .

$x + 15 = 20$

Step 4

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

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Step 4.1

Subtract $15$ from both sides of the equation.

$x = 20 - 15$

Step 4.2

Subtract $15$ from $20$ .

$x = 5$