Solve 5(x-1)+4geq-3(x+4)-1

$$5 ( x - 1 ) + 4 \geq - 3 ( x + 4 ) - 1$$

Solve for x

$$x\geq -\frac{3}{2}$$

Solution Steps

Use the distributive property to multiply 5 by x-1.

$$5x-5+4\geq -3\left(x+4\right)-1$$

Add -5 and 4 to get -1.

$$5x-1\geq -3\left(x+4\right)-1$$

Use the distributive property to multiply -3 by x+4.

$$5x-1\geq -3x-12-1$$

Subtract 1 from -12 to get -13.

$$5x-1\geq -3x-13$$

Add 3x to both sides.

$$5x-1+3x\geq -13$$

Combine 5x and 3x to get 8x.

$$8x-1\geq -13$$

Add 1 to both sides.

$$8x\geq -13+1$$

Add -13 and 1 to get -12.

$$8x\geq -12$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$x\geq \frac{-12}{8}$$

Reduce the fraction \frac{-12}{8} to lowest terms by extracting and canceling out 4.

$$x\geq -\frac{3}{2}$$