Solve |6x-2/7|=4

$$| \frac { 6 x - 2 } { 7 } | = 4$$

Solve for x

$$x = -\frac{13}{3} = -4\frac{1}{3} \approx -4.333333333$$

$$x=5$$

Steps Using Definition of Absolute Value

Divide each term of 6x-2 by 7 to get \frac{6}{7}x-\frac{2}{7}.

$$|\frac{6}{7}x-\frac{2}{7}|=4$$

Use the definition of absolute value.

$$\frac{6}{7}x-\frac{2}{7}=4 \frac{6}{7}x-\frac{2}{7}=-4$$

Add \frac{2}{7} to both sides of the equation.

$$\frac{6}{7}x=\frac{30}{7} \frac{6}{7}x=-\frac{26}{7}$$

Divide both sides of the equation by \frac{6}{7}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=5 x=-\frac{13}{3}$$