Solve 6-2(x+1)leq3(1-2x)

$$6 - 2 ( x + 1 ) \leq 3 ( 1 - 2 x )$$

Solve for x

$$x\leq -\frac{1}{4}$$

Solution Steps

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

$$6-2x-2\leq 3\left(1-2x\right)$$

Subtract 2 from 6 to get 4.

$$4-2x\leq 3\left(1-2x\right)$$

Use the distributive property to multiply 3 by 1-2x.

$$4-2x\leq 3-6x$$

Add 6x to both sides.

$$4-2x+6x\leq 3$$

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

$$4+4x\leq 3$$

Subtract 4 from both sides.

$$4x\leq 3-4$$

Subtract 4 from 3 to get -1.

$$4x\leq -1$$

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

$$x\leq -\frac{1}{4}$$