Solve x/5-4x/10geqx+8/3

$$\frac { x } { 5 } - \frac { 4 x } { 10 } \geq \frac { x + 8 } { 3 }$$

Solve for x

$$x\leq -5$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,10,3. Since 30 is positive, the inequality direction remains the same.

$$6x-3\times 4x\geq 10\left(x+8\right)$$

Multiply -3 and 4 to get -12.

$$6x-12x\geq 10\left(x+8\right)$$

Combine 6x and -12x to get -6x.

$$-6x\geq 10\left(x+8\right)$$

Use the distributive property to multiply 10 by x+8.

$$-6x\geq 10x+80$$

Subtract 10x from both sides.

$$-6x-10x\geq 80$$

Combine -6x and -10x to get -16x.

$$-16x\geq 80$$

Divide both sides by -16. Since -16 is negative, the inequality direction is changed.

$$x\leq \frac{80}{-16}$$

Divide 80 by -16 to get -5.

$$x\leq -5$$