Algebra Examples

$- \frac{4 x}{7} > 10$

Step 1

Solve $x < - \frac{35}{2}$ .

Tap for more steps...

Step 1.1

Divide each term in $- \frac{4 x}{7} > 10$ by $- 1$ and simplify.

Tap for more steps...

Step 1.1.1

Divide each term in $- \frac{4 x}{7} > 10$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{4 x}{7}}{- 1} < \frac{10}{- 1}$

Step 1.1.2

Simplify the left side.

Tap for more steps...

Step 1.1.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{4 x}{7}}{1} < \frac{10}{- 1}$

Step 1.1.2.2

Divide $\frac{4 x}{7}$ by $1$ .

$\frac{4 x}{7} < \frac{10}{- 1}$

Step 1.1.3

Simplify the right side.

Tap for more steps...

Step 1.1.3.1

Divide $10$ by $- 1$ .

$\frac{4 x}{7} < - 10$

Step 1.2

Multiply both sides by $7$ .

$\frac{4 x}{7} \cdot 7 < - 10 \cdot 7$

Step 1.3

Simplify.

Tap for more steps...

Step 1.3.1

Simplify the left side.

Tap for more steps...

Step 1.3.1.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 1.3.1.1.1

Cancel the common factor.

$\frac{4 x}{7} \cdot 7 < - 10 \cdot 7$

Step 1.3.1.1.2

Rewrite the expression.

$4 x < - 10 \cdot 7$

Step 1.3.2

Simplify the right side.

Tap for more steps...

Step 1.3.2.1

Multiply $- 10$ by $7$ .

$4 x < - 70$

Step 1.4

Divide each term in $4 x < - 70$ by $4$ and simplify.

Tap for more steps...

Step 1.4.1

Divide each term in $4 x < - 70$ by $4$ .

$\frac{4 x}{4} < \frac{- 70}{4}$

Step 1.4.2

Simplify the left side.

Tap for more steps...

Step 1.4.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} < \frac{- 70}{4}$

Step 1.4.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 70}{4}$

Step 1.4.3

Simplify the right side.

Tap for more steps...

Step 1.4.3.1

Cancel the common factor of $- 70$ and $4$ .

Tap for more steps...

Step 1.4.3.1.1

Factor $2$ out of $- 70$ .

$x < \frac{2 (- 35)}{4}$

Step 1.4.3.1.2

Cancel the common factors.

Tap for more steps...

Step 1.4.3.1.2.1

Factor $2$ out of $4$ .

$x < \frac{2 \cdot - 35}{2 \cdot 2}$

Step 1.4.3.1.2.2

Cancel the common factor.

$x < \frac{2 \cdot - 35}{2 \cdot 2}$

Step 1.4.3.1.2.3

Rewrite the expression.

$x < \frac{- 35}{2}$

Step 1.4.3.2

Move the negative in front of the fraction.

$x < - \frac{35}{2}$

Step 2

Use the inequality $x < - \frac{35}{2}$ to build the set notation.

${x | x < - \frac{35}{2}}$

Step 3