Solve 20x/3-40x+10/5geq30

$$\frac { 20 x } { 3 } - \frac { 40 x + 10 } { 5 } \geq 30$$

Solve for x

$$x\leq -24$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 3,5. Since 15 is positive, the inequality direction remains the same.

$$5\times 20x-3\left(40x+10\right)\geq 450$$

Multiply 5 and 20 to get 100.

$$100x-3\left(40x+10\right)\geq 450$$

Use the distributive property to multiply -3 by 40x+10.

$$100x-120x-30\geq 450$$

Combine 100x and -120x to get -20x.

$$-20x-30\geq 450$$

Add 30 to both sides.

$$-20x\geq 450+30$$

Add 450 and 30 to get 480.

$$-20x\geq 480$$

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

$$x\leq \frac{480}{-20}$$

Divide 480 by -20 to get -24.

$$x\leq -24$$