Solve 1-3x-4-9x/7geq5-8x/5

$$1 - 3 x - \frac { 4 - 9 x } { 7 } \geq \frac { 5 - 8 x } { 5 }$$

Solve for x

$$x\leq -5$$

Solution Steps

Multiply both sides of the equation by 35, the least common multiple of 7,5. Since 35 is positive, the inequality direction remains the same.

$$35-105x-5\left(4-9x\right)\geq 7\left(5-8x\right)$$

Use the distributive property to multiply -5 by 4-9x.

$$35-105x-20+45x\geq 7\left(5-8x\right)$$

Subtract 20 from 35 to get 15.

$$15-105x+45x\geq 7\left(5-8x\right)$$

Combine -105x and 45x to get -60x.

$$15-60x\geq 7\left(5-8x\right)$$

Use the distributive property to multiply 7 by 5-8x.

$$15-60x\geq 35-56x$$

Add 56x to both sides.

$$15-60x+56x\geq 35$$

Combine -60x and 56x to get -4x.

$$15-4x\geq 35$$

Subtract 15 from both sides.

$$-4x\geq 35-15$$

Subtract 15 from 35 to get 20.

$$-4x\geq 20$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x\leq \frac{20}{-4}$$

Divide 20 by -4 to get -5.

$$x\leq -5$$