Solve 12-4/5(5x-15)leq4/7(14x+105)

$$12 - \frac { 4 } { 5 } ( 5 x - 15 ) \leq \frac { 4 } { 7 } ( 14 x + 105 )$$

Solve for x

$$x\geq -3$$

Solution Steps

Use the distributive property to multiply -\frac{4}{5} by 5x-15.

$$12-\frac{4}{5}\times 5x-\frac{4}{5}\left(-15\right)\leq \frac{4}{7}\left(14x+105\right)$$

Cancel out 5 and 5.

$$12-4x-\frac{4}{5}\left(-15\right)\leq \frac{4}{7}\left(14x+105\right)$$

Express -\frac{4}{5}\left(-15\right) as a single fraction.

$$12-4x+\frac{-4\left(-15\right)}{5}\leq \frac{4}{7}\left(14x+105\right)$$

Multiply -4 and -15 to get 60.

$$12-4x+\frac{60}{5}\leq \frac{4}{7}\left(14x+105\right)$$

Divide 60 by 5 to get 12.

$$12-4x+12\leq \frac{4}{7}\left(14x+105\right)$$

Add 12 and 12 to get 24.

$$24-4x\leq \frac{4}{7}\left(14x+105\right)$$

Use the distributive property to multiply \frac{4}{7} by 14x+105.

$$24-4x\leq \frac{4}{7}\times 14x+\frac{4}{7}\times 105$$

Express \frac{4}{7}\times 14 as a single fraction.

$$24-4x\leq \frac{4\times 14}{7}x+\frac{4}{7}\times 105$$

Multiply 4 and 14 to get 56.

$$24-4x\leq \frac{56}{7}x+\frac{4}{7}\times 105$$

Divide 56 by 7 to get 8.

$$24-4x\leq 8x+\frac{4}{7}\times 105$$

Express \frac{4}{7}\times 105 as a single fraction.

$$24-4x\leq 8x+\frac{4\times 105}{7}$$

Multiply 4 and 105 to get 420.

$$24-4x\leq 8x+\frac{420}{7}$$

Divide 420 by 7 to get 60.

$$24-4x\leq 8x+60$$

Subtract 8x from both sides.

$$24-4x-8x\leq 60$$

Combine -4x and -8x to get -12x.

$$24-12x\leq 60$$

Subtract 24 from both sides.

$$-12x\leq 60-24$$

Subtract 24 from 60 to get 36.

$$-12x\leq 36$$

Divide both sides by -12. Since -12 is negative, the inequality direction is changed.

$$x\geq \frac{36}{-12}$$

Divide 36 by -12 to get -3.

$$x\geq -3$$