Algebra Examples

$\frac{7}{8} x + 1 = 2 - \frac{1}{4} x$

Step 1

Combine $\frac{7}{8}$ and $x$ .

$\frac{7 x}{8} + 1 = 2 - \frac{1}{4} x$

Step 2

Combine $x$ and $\frac{1}{4}$ .

$\frac{7 x}{8} + 1 = 2 - \frac{x}{4}$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Add $\frac{x}{4}$ to both sides of the equation.

$\frac{7 x}{8} + 1 + \frac{x}{4} = 2$

Step 3.2

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

$\frac{7 x}{8} + \frac{x}{4} \cdot \frac{2}{2} + 1 = 2$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{x}{4}$ by $\frac{2}{2}$ .

$\frac{7 x}{8} + \frac{x \cdot 2}{4 \cdot 2} + 1 = 2$

Step 3.3.2

Multiply $4$ by $2$ .

$\frac{7 x}{8} + \frac{x \cdot 2}{8} + 1 = 2$

Step 3.4

Combine the numerators over the common denominator.

$\frac{7 x + x \cdot 2}{8} + 1 = 2$

Step 3.5

Add $7 x$ and $x \cdot 2$ .

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Step 3.5.1

Reorder $x$ and $2$ .

$\frac{7 x + 2 \cdot x}{8} + 1 = 2$

Step 3.5.2

Add $7 x$ and $2 \cdot x$ .

$\frac{9 x}{8} + 1 = 2$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$\frac{9 x}{8} = 2 - 1$

Step 4.2

Subtract $1$ from $2$ .

$\frac{9 x}{8} = 1$

Step 5

Multiply both sides of the equation by $\frac{8}{9}$ .

$\frac{8}{9} \cdot \frac{9 x}{8} = \frac{8}{9} \cdot 1$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{8}{9} \cdot \frac{9 x}{8}$ .

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Step 6.1.1.1

Cancel the common factor of $8$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{8}{9} \cdot \frac{9 x}{8} = \frac{8}{9} \cdot 1$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 x) = \frac{8}{9} \cdot 1$

Step 6.1.1.2

Cancel the common factor of $9$ .

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Step 6.1.1.2.1

Factor $9$ out of $9 x$ .

$\frac{1}{9} (9 (x)) = \frac{8}{9} \cdot 1$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 x) = \frac{8}{9} \cdot 1$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{8}{9} \cdot 1$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $\frac{8}{9}$ by $1$ .

$x = \frac{8}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{9}$

Decimal Form:

$x = 0.\overline{8}$