Solve 5(x+2)-4(x-6)<8(x+3)

$$5 ( x + 2 ) - 4 ( x - 6 ) < 8 ( x + 3 )$$

Solve for x

$$x>\frac{10}{7}$$

Solution Steps

Use the distributive property to multiply 5 by x+2.

$$5x+10-4\left(x-6\right)<8\left(x+3\right)$$

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

$$5x+10-4x+24<8\left(x+3\right)$$

Combine 5x and -4x to get x.

$$x+10+24<8\left(x+3\right)$$

Add 10 and 24 to get 34.

$$x+34<8\left(x+3\right)$$

Use the distributive property to multiply 8 by x+3.

$$x+34<8x+24$$

Subtract 8x from both sides.

$$x+34-8x<24$$

Combine x and -8x to get -7x.

$$-7x+34<24$$

Subtract 34 from both sides.

$$-7x<24-34$$

Subtract 34 from 24 to get -10.

$$-7x<-10$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x>\frac{-10}{-7}$$

Fraction \frac{-10}{-7} can be simplified to \frac{10}{7} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{10}{7}$$