Solve x/4-1-x/3leq1+3x/2

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

Solve for x

$$x\geq -\frac{16}{11}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3,2. Since 12 is positive, the inequality direction remains the same.

$$3x-4\left(1-x\right)\leq 12+6\times 3x$$

Use the distributive property to multiply -4 by 1-x.

$$3x-4+4x\leq 12+6\times 3x$$

Combine 3x and 4x to get 7x.

$$7x-4\leq 12+6\times 3x$$

Multiply 6 and 3 to get 18.

$$7x-4\leq 12+18x$$

Subtract 18x from both sides.

$$7x-4-18x\leq 12$$

Combine 7x and -18x to get -11x.

$$-11x-4\leq 12$$

Add 4 to both sides.

$$-11x\leq 12+4$$

Add 12 and 4 to get 16.

$$-11x\leq 16$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$x\geq -\frac{16}{11}$$