Solve 3[x-2(x-7)]leq4x

$$3 [ x - 2 ( x - 7 ) ] \leq 4 x$$

Solve for x

$$x\geq 6$$

Solution Steps

Use the distributive property to multiply -2 by x-7.

$$3\left(x-2x+14\right)\leq 4x$$

Combine x and -2x to get -x.

$$3\left(-x+14\right)\leq 4x$$

Use the distributive property to multiply 3 by -x+14.

$$-3x+42\leq 4x$$

Subtract 4x from both sides.

$$-3x+42-4x\leq 0$$

Combine -3x and -4x to get -7x.

$$-7x+42\leq 0$$

Subtract 42 from both sides. Anything subtracted from zero gives its negation.

$$-7x\leq -42$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x\geq \frac{-42}{-7}$$

Divide -42 by -7 to get 6.

$$x\geq 6$$