Solve 4left(x-2right)-3geq-3left(-2+6right)+2

$$4 \left( x-2 \right) -3 \geq -3 \left( -2+6 \right) +2$$

Solve for x

$$x\geq \frac{1}{4}$$

Solution Steps

Use the distributive property to multiply 4 by x-2.

$$4x-8-3\geq -3\left(-2+6\right)+2$$

Subtract 3 from -8 to get -11.

$$4x-11\geq -3\left(-2+6\right)+2$$

Add -2 and 6 to get 4.

$$4x-11\geq -3\times 4+2$$

Multiply -3 and 4 to get -12.

$$4x-11\geq -12+2$$

Add -12 and 2 to get -10.

$$4x-11\geq -10$$

Add 11 to both sides.

$$4x\geq -10+11$$

Add -10 and 11 to get 1.

$$4x\geq 1$$

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

$$x\geq \frac{1}{4}$$