Solution - Absolute value equations

$$-8a-3=-\left(-8a-3\right)$$

Expand the parentheses:

$$-8a-3=8a+3$$

Subtract $$$$ from both sides:

$$\left(-8a-3\right)-8a=\left(8a+3\right)-8a$$

Group like terms:

$$\left(-8a-8a\right)-3=\left(8a+3\right)-8a$$

Simplify the arithmetic:

$$-16a-3=\left(8a+3\right)-8a$$

Group like terms:

$$-16a-3=\left(8a-8a\right)+3$$

Simplify the arithmetic:

$$-16a-3=3$$

Add $$$$ to both sides:

$$\left(-16a-3\right)+3=3+3$$

Simplify the arithmetic:

$$-16a=3+3$$

Simplify the arithmetic:

$$-16a=6$$

Divide both sides by :

$$\frac{\left(-16a\right)}{-16}=\frac{6}{-16}$$

Cancel out the negatives:

$$\frac{16a}{16}=\frac{6}{-16}$$

Simplify the fraction:

$$a=\frac{6}{-16}$$

Move the negative sign from the denominator to the numerator:

$$a=\frac{-6}{16}$$

Find the greatest common factor of the numerator and denominator:

$$a=\frac{\left(-3·2\right)}{\left(8·2\right)}$$

Factor out and cancel the greatest common factor:

$$a=\frac{-3}{8}$$

$$-8a-3=-\left(-\left(-8a-3\right)\right)$$

Resolve the double minus:

$$-8a-3=-8a-3$$

Add $$$$ to both sides:

$$\left(-8a-3\right)+8a=\left(-8a-3\right)+8a$$

Group like terms:

$$\left(-8a+8a\right)-3=\left(-8a-3\right)+8a$$

Simplify the arithmetic:

$$-3=\left(-8a-3\right)+8a$$

Group like terms:

$$-3=\left(-8a+8a\right)-3$$

Simplify the arithmetic:

$$-3=-3$$