Solve 4-(2x-1)leq3(4x+1

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

Solve for x

$$x\geq \frac{1}{7}$$

Solution Steps

To find the opposite of 2x-1, find the opposite of each term.

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

The opposite of -1 is 1.

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

Add 4 and 1 to get 5.

$$5-2x\leq 3\left(4x+1\right)$$

Use the distributive property to multiply 3 by 4x+1.

$$5-2x\leq 12x+3$$

Subtract 12x from both sides.

$$5-2x-12x\leq 3$$

Combine -2x and -12x to get -14x.

$$5-14x\leq 3$$

Subtract 5 from both sides.

$$-14x\leq 3-5$$

Subtract 5 from 3 to get -2.

$$-14x\leq -2$$

Divide both sides by -14. Since -14 is negative, the inequality direction is changed.

$$x\geq \frac{-2}{-14}$$

Reduce the fraction \frac{-2}{-14} to lowest terms by extracting and canceling out -2.

$$x\geq \frac{1}{7}$$