Solution - Absolute value equations

$$\left(x-7\right)=-5x-3$$

Add $$$$ to both sides:

$$\left(x-7\right)+5x=\left(-5x-3\right)+5x$$

Group like terms:

$$\left(x+5x\right)-7=\left(-5x-3\right)+5x$$

Simplify the arithmetic:

$$6x-7=\left(-5x-3\right)+5x$$

Group like terms:

$$6x-7=\left(-5x+5x\right)-3$$

Simplify the arithmetic:

$$6x-7=-3$$

Add $$$$ to both sides:

$$\left(6x-7\right)+7=-3+7$$

Simplify the arithmetic:

$$6x=-3+7$$

Simplify the arithmetic:

$$6x=4$$

Divide both sides by :

$$\frac{\left(6x\right)}{6}=\frac{4}{6}$$

Simplify the fraction:

$$x=\frac{4}{6}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(2·2\right)}{\left(3·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=\frac{2}{3}$$

$$\left(x-7\right)=5x+3$$

Subtract $$$$ from both sides:

$$\left(x-7\right)-5x=\left(5x+3\right)-5x$$

Group like terms:

$$\left(x-5x\right)-7=\left(5x+3\right)-5x$$

Simplify the arithmetic:

$$-4x-7=\left(5x+3\right)-5x$$

Group like terms:

$$-4x-7=\left(5x-5x\right)+3$$

Simplify the arithmetic:

$$-4x-7=3$$

Add $$$$ to both sides:

$$\left(-4x-7\right)+7=3+7$$

Simplify the arithmetic:

$$-4x=3+7$$

Simplify the arithmetic:

$$-4x=10$$

Divide both sides by :

$$\frac{\left(-4x\right)}{-4}=\frac{10}{-4}$$

Cancel out the negatives:

$$\frac{4x}{4}=\frac{10}{-4}$$

Simplify the fraction:

$$x=\frac{10}{-4}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-10}{4}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-5·2\right)}{\left(2·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=\frac{-5}{2}$$