Solve 10-4(x-3)leq2(x-1)

$$10 - 4 ( x - 3 ) \leq 2 ( x - 1 )$$

Solve for x

$$x\geq 4$$

Solution Steps

Use the distributive property to multiply -4 by x-3.

$$10-4x+12\leq 2\left(x-1\right)$$

Add 10 and 12 to get 22.

$$22-4x\leq 2\left(x-1\right)$$

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

$$22-4x\leq 2x-2$$

Subtract 2x from both sides.

$$22-4x-2x\leq -2$$

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

$$22-6x\leq -2$$

Subtract 22 from both sides.

$$-6x\leq -2-22$$

Subtract 22 from -2 to get -24.

$$-6x\leq -24$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x\geq \frac{-24}{-6}$$

Divide -24 by -6 to get 4.

$$x\geq 4$$