Algebra Examples

$9 (4 - 2 x) + 7 x < 6 (8 + 3 x)$

Step 1

Solve $x > - \frac{12}{29}$ .

Tap for more steps...

Simplify $9 (4 - 2 x) + 7 x$ .

Tap for more steps...

Simplify each term.

Tap for more steps...

Apply the distributive property.

$9 \cdot 4 + 9 (- 2 x) + 7 x < 6 (8 + 3 x)$

Multiply $9$ by $4$ .

$36 + 9 (- 2 x) + 7 x < 6 (8 + 3 x)$

Multiply $- 2$ by $9$ .

$36 - 18 x + 7 x < 6 (8 + 3 x)$

Add $- 18 x$ and $7 x$ .

$36 - 11 x < 6 (8 + 3 x)$

Simplify $6 (8 + 3 x)$ .

Tap for more steps...

Apply the distributive property.

$36 - 11 x < 6 \cdot 8 + 6 (3 x)$

Multiply.

Tap for more steps...

Multiply $6$ by $8$ .

$36 - 11 x < 48 + 6 (3 x)$

Multiply $3$ by $6$ .

$36 - 11 x < 48 + 18 x$

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

Tap for more steps...

Subtract $18 x$ from both sides of the inequality.

$36 - 11 x - 18 x < 48$

Subtract $18 x$ from $- 11 x$ .

$36 - 29 x < 48$

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

Tap for more steps...

Subtract $36$ from both sides of the inequality.

$- 29 x < 48 - 36$

Subtract $36$ from $48$ .

$- 29 x < 12$

Divide each term in $- 29 x < 12$ by $- 29$ and simplify.

Tap for more steps...

Divide each term in $- 29 x < 12$ by $- 29$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 29 x}{- 29} > \frac{12}{- 29}$

Simplify the left side.

Tap for more steps...

Cancel the common factor of $- 29$ .

Tap for more steps...

Cancel the common factor.

$\frac{- 29 x}{- 29} > \frac{12}{- 29}$

Divide $x$ by $1$ .

$x > \frac{12}{- 29}$

Simplify the right side.

Tap for more steps...

Move the negative in front of the fraction.

$x > - \frac{12}{29}$

Step 2

Use the inequality $x > - \frac{12}{29}$ to build the set notation.

${x | x > - \frac{12}{29}}$

Step 3