Solve 2-3x/2geq5x-16/3

$$\frac { 2 - 3 x } { 2 } \geq \frac { 5 x - 16 } { 3 }$$

Solve for x

$$x\leq 2$$

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.

$$3\left(2-3x\right)\geq 2\left(5x-16\right)$$

Use the distributive property to multiply 3 by 2-3x.

$$6-9x\geq 2\left(5x-16\right)$$

Use the distributive property to multiply 2 by 5x-16.

$$6-9x\geq 10x-32$$

Subtract 10x from both sides.

$$6-9x-10x\geq -32$$

Combine -9x and -10x to get -19x.

$$6-19x\geq -32$$

Subtract 6 from both sides.

$$-19x\geq -32-6$$

Subtract 6 from -32 to get -38.

$$-19x\geq -38$$

Divide both sides by -19. Since -19 is negative, the inequality direction is changed.

$$x\leq \frac{-38}{-19}$$

Divide -38 by -19 to get 2.

$$x\leq 2$$