Solve x-3/2+5-2x/3leq4

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

Solve for x

$$x\geq -23$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$3\left(x-3\right)+2\left(5-2x\right)\leq 24$$

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

$$3x-9+2\left(5-2x\right)\leq 24$$

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

$$3x-9+10-4x\leq 24$$

Add -9 and 10 to get 1.

$$3x+1-4x\leq 24$$

Combine 3x and -4x to get -x.

$$-x+1\leq 24$$

Subtract 1 from both sides.

$$-x\leq 24-1$$

Subtract 1 from 24 to get 23.

$$-x\leq 23$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\geq -23$$