Precalculus Examples

$\frac{1}{2} x - \frac{5}{7} = 1 - \frac{x}{2}$

Step 1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} - \frac{5}{7} = 1 - \frac{x}{2}$

Step 2

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

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Step 2.1

Add $\frac{x}{2}$ to both sides of the equation.

$\frac{x}{2} - \frac{5}{7} + \frac{x}{2} = 1$

Step 2.2

Combine the numerators over the common denominator.

$\frac{x + x}{2} + \frac{- 5}{7} = 1$

Step 2.3

Add $x$ and $x$ .

$\frac{2 x}{2} + \frac{- 5}{7} = 1$

Step 2.4

Simplify each term.

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Step 2.4.1

Cancel the common factor of $2$ .

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Step 2.4.1.1

Cancel the common factor.

$\frac{2 x}{2} + \frac{- 5}{7} = 1$

Step 2.4.1.2

Divide $x$ by $1$ .

$x + \frac{- 5}{7} = 1$

Step 2.4.2

Move the negative in front of the fraction.

$x - \frac{5}{7} = 1$

Step 3

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

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Step 3.1

Add $\frac{5}{7}$ to both sides of the equation.

$x = 1 + \frac{5}{7}$

Step 3.2

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

$x = \frac{7}{7} + \frac{5}{7}$

Step 3.3

Combine the numerators over the common denominator.

$x = \frac{7 + 5}{7}$

Step 3.4

Add $7$ and $5$ .

$x = \frac{12}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{12}{7}$

Decimal Form:

$x = 1.\overline{714285}$

Mixed Number Form:

$x = 1 \frac{5}{7}$