Solve 3x-5/2-2(x-1)/3geq3x

$$\frac { 3 x - 5 } { 2 } - \frac { 2 ( x - 1 ) } { 3 } \geq 3 x$$

Solve for x

$$x\leq -\frac{11}{13}$$

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.

$$3\left(3x-5\right)-2\times 2\left(x-1\right)\geq 18x$$

Use the distributive property to multiply 3 by 3x-5.

$$9x-15-2\times 2\left(x-1\right)\geq 18x$$

Multiply -2 and 2 to get -4.

$$9x-15-4\left(x-1\right)\geq 18x$$

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

$$9x-15-4x+4\geq 18x$$

Combine 9x and -4x to get 5x.

$$5x-15+4\geq 18x$$

Add -15 and 4 to get -11.

$$5x-11\geq 18x$$

Subtract 18x from both sides.

$$5x-11-18x\geq 0$$

Combine 5x and -18x to get -13x.

$$-13x-11\geq 0$$

Add 11 to both sides. Anything plus zero gives itself.

$$-13x\geq 11$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\leq -\frac{11}{13}$$