Solve 10-2x/3geq2(3x-5)

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

Solve for x

$$x\leq 2$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$10-2x\geq 6\left(3x-5\right)$$

Use the distributive property to multiply 6 by 3x-5.

$$10-2x\geq 18x-30$$

Subtract 18x from both sides.

$$10-2x-18x\geq -30$$

Combine -2x and -18x to get -20x.

$$10-20x\geq -30$$

Subtract 10 from both sides.

$$-20x\geq -30-10$$

Subtract 10 from -30 to get -40.

$$-20x\geq -40$$

Divide both sides by -20. Since -20 is negative, the inequality direction is changed.

$$x\leq \frac{-40}{-20}$$

Divide -40 by -20 to get 2.

$$x\leq 2$$