Solve 4-3x/5-x+2/3+xleq-1

$$\frac { 4 - 3 x } { 5 } - \frac { x + 2 } { 3 } + x \leq - 1$$

Solve for x

$$x\leq -17$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 5,3. Since 15 is positive, the inequality direction remains the same.

$$3\left(4-3x\right)-5\left(x+2\right)+15x\leq -15$$

Use the distributive property to multiply 3 by 4-3x.

$$12-9x-5\left(x+2\right)+15x\leq -15$$

Use the distributive property to multiply -5 by x+2.

$$12-9x-5x-10+15x\leq -15$$

Combine -9x and -5x to get -14x.

$$12-14x-10+15x\leq -15$$

Subtract 10 from 12 to get 2.

$$2-14x+15x\leq -15$$

Combine -14x and 15x to get x.

$$2+x\leq -15$$

Subtract 2 from both sides.

$$x\leq -15-2$$

Subtract 2 from -15 to get -17.

$$x\leq -17$$