Solve 3(2x-3)geq2(x+5)-1

$$3(2x-3) \geq 2(x+5)-1$$

Solve for x

$$x\geq \frac{9}{2}$$

Solution Steps

Use the distributive property to multiply 3 by 2x-3.

$$6x-9\geq 2\left(x+5\right)-1$$

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

$$6x-9\geq 2x+10-1$$

Subtract 1 from 10 to get 9.

$$6x-9\geq 2x+9$$

Subtract 2x from both sides.

$$6x-9-2x\geq 9$$

Combine 6x and -2x to get 4x.

$$4x-9\geq 9$$

Add 9 to both sides.

$$4x\geq 9+9$$

Add 9 and 9 to get 18.

$$4x\geq 18$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x\geq \frac{18}{4}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$x\geq \frac{9}{2}$$