Solve 3[x-2(x-1)]leq4x

$$3 [ x - 2 ( x - 1 ) ] \leq 4 x$$

Solve for x

$$x\geq \frac{6}{7}$$

Solution Steps

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

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

Combine x and -2x to get -x.

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

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

$$-3x+6\leq 4x$$

Subtract 4x from both sides.

$$-3x+6-4x\leq 0$$

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

$$-7x+6\leq 0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-7x\leq -6$$

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

$$x\geq \frac{-6}{-7}$$

Fraction \frac{-6}{-7} can be simplified to \frac{6}{7} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{6}{7}$$