Solve 4x+6/5geq8x-8/6

$$\frac { 4 x + 6 } { 5 } \geq \frac { 8 x - 8 } { 6 }$$

Solve for x

$$x\leq \frac{19}{4}$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,6. Since 30 is positive, the inequality direction remains the same.

$$6\left(4x+6\right)\geq 5\left(8x-8\right)$$

Use the distributive property to multiply 6 by 4x+6.

$$24x+36\geq 5\left(8x-8\right)$$

Use the distributive property to multiply 5 by 8x-8.

$$24x+36\geq 40x-40$$

Subtract 40x from both sides.

$$24x+36-40x\geq -40$$

Combine 24x and -40x to get -16x.

$$-16x+36\geq -40$$

Subtract 36 from both sides.

$$-16x\geq -40-36$$

Subtract 36 from -40 to get -76.

$$-16x\geq -76$$

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

$$x\leq \frac{-76}{-16}$$

Reduce the fraction \frac{-76}{-16} to lowest terms by extracting and canceling out -4.

$$x\leq \frac{19}{4}$$