Algebra Examples

$x - \frac{1}{7} > \frac{1}{8}$

Step 1

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

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Step 1.1

Add $\frac{1}{7}$ to both sides of the inequality.

$x > \frac{1}{8} + \frac{1}{7}$

Step 1.2

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x > \frac{1}{8} \cdot \frac{7}{7} + \frac{1}{7}$

Step 1.3

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$x > \frac{1}{8} \cdot \frac{7}{7} + \frac{1}{7} \cdot \frac{8}{8}$

Step 1.4

Write each expression with a common denominator of $56$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{8}$ by $\frac{7}{7}$ .

$x > \frac{7}{8 \cdot 7} + \frac{1}{7} \cdot \frac{8}{8}$

Step 1.4.2

Multiply $8$ by $7$ .

$x > \frac{7}{56} + \frac{1}{7} \cdot \frac{8}{8}$

Step 1.4.3

Multiply $\frac{1}{7}$ by $\frac{8}{8}$ .

$x > \frac{7}{56} + \frac{8}{7 \cdot 8}$

Step 1.4.4

Multiply $7$ by $8$ .

$x > \frac{7}{56} + \frac{8}{56}$

Step 1.5

Combine the numerators over the common denominator.

$x > \frac{7 + 8}{56}$

Step 1.6

Add $7$ and $8$ .

$x > \frac{15}{56}$

Step 2

Use the inequality $x > \frac{15}{56}$ to build the set notation.

${x | x > \frac{15}{56}}$

Step 3