Solve -2left|x+3right|+4left|x+3right|=15-5left|x+3right|-1

$$-2 \left| x+3 \right| +4 \left| x+3 \right| =15-5 \left| x+3 \right| -1$$

Solve for x

$$x=-5$$

$$x=-1$$

Steps Using Definition of Absolute Value

Combine -2|x+3| and 4|x+3| to get 2|x+3|.

$$2|x+3|=15-5|x+3|-1$$

Subtract 15-5|x+3| from both sides.

$$2|x+3|-\left(15-5|x+3|\right)=-1$$

To find the opposite of 15-5|x+3|, find the opposite of each term.

$$2|x+3|-15-\left(-5|x+3|\right)=-1$$

The opposite of -5|x+3| is 5|x+3|.

$$2|x+3|-15+5|x+3|=-1$$

Combine 2|x+3| and 5|x+3| to get 7|x+3|.

$$7|x+3|-15=-1$$

Add 15 to both sides.

$$7|x+3|=-1+15$$

Add -1 and 15 to get 14.

$$7|x+3|=14$$

Divide both sides by 7.

$$|x+3|=\frac{14}{7}$$

Divide 14 by 7 to get 2.

$$|x+3|=2$$

Use the definition of absolute value.

$$x+3=2 x+3=-2$$

Subtract 3 from both sides of the equation.

$$x=-1 x=-5$$