Solve x-5/3-xgeq-3(x-1)

$$\frac { x - 5 } { 3 } - x \geq - 3 ( x - 1 )$$

Solve for x

$$x\geq 2$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$x-5-3x\geq -9\left(x-1\right)$$

Combine x and -3x to get -2x.

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

Use the distributive property to multiply -9 by x-1.

$$-2x-5\geq -9x+9$$

Add 9x to both sides.

$$-2x-5+9x\geq 9$$

Combine -2x and 9x to get 7x.

$$7x-5\geq 9$$

Add 5 to both sides.

$$7x\geq 9+5$$

Add 9 and 5 to get 14.

$$7x\geq 14$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x\geq \frac{14}{7}$$

Divide 14 by 7 to get 2.

$$x\geq 2$$