Solve 2(x-3)/3-3(2x-5)/2geq10

$$\frac { 2 ( x - 3 ) } { 3 } - \frac { 3 ( 2 x - 5 ) } { 2 } \geq 10$$

Solve for x

$$x\leq -\frac{27}{14}$$

Solution Steps

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

$$2\times 2\left(x-3\right)-3\times 3\left(2x-5\right)\geq 60$$

Multiply 2 and 2 to get 4.

$$4\left(x-3\right)-3\times 3\left(2x-5\right)\geq 60$$

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

$$4x-12-3\times 3\left(2x-5\right)\geq 60$$

Multiply -3 and 3 to get -9.

$$4x-12-9\left(2x-5\right)\geq 60$$

Use the distributive property to multiply -9 by 2x-5.

$$4x-12-18x+45\geq 60$$

Combine 4x and -18x to get -14x.

$$-14x-12+45\geq 60$$

Add -12 and 45 to get 33.

$$-14x+33\geq 60$$

Subtract 33 from both sides.

$$-14x\geq 60-33$$

Subtract 33 from 60 to get 27.

$$-14x\geq 27$$

Divide both sides by -14. Since -14 is negative, the inequality direction is changed.

$$x\leq -\frac{27}{14}$$