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

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

Solve for x

$$x\geq -1$$

Solution Steps

Use the distributive property to multiply 3 by 2x-1.

$$6x-3+5\geq -2\left(x+3\right)$$

Add -3 and 5 to get 2.

$$6x+2\geq -2\left(x+3\right)$$

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

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

Add 2x to both sides.

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

Combine 6x and 2x to get 8x.

$$8x+2\geq -6$$

Subtract 2 from both sides.

$$8x\geq -6-2$$

Subtract 2 from -6 to get -8.

$$8x\geq -8$$

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

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

Divide -8 by 8 to get -1.

$$x\geq -1$$