Solve 4(x-1)-2x+5/2geq-14

$$4(x-1)- \frac{ 2x+5 }{ 2 } \geq -14$$

Solve for x

$$x\geq -\frac{5}{2}$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$8\left(x-1\right)-\left(2x+5\right)\geq -28$$

Use the distributive property to multiply 8 by x-1.

$$8x-8-\left(2x+5\right)\geq -28$$

To find the opposite of 2x+5, find the opposite of each term.

$$8x-8-2x-5\geq -28$$

Combine 8x and -2x to get 6x.

$$6x-8-5\geq -28$$

Subtract 5 from -8 to get -13.

$$6x-13\geq -28$$

Add 13 to both sides.

$$6x\geq -28+13$$

Add -28 and 13 to get -15.

$$6x\geq -15$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$x\geq \frac{-15}{6}$$

Reduce the fraction \frac{-15}{6} to lowest terms by extracting and canceling out 3.

$$x\geq -\frac{5}{2}$$