Question

Solve the equation. $$|x+3|=6$$

Short answer

The solutions to the equation \( |x+3|=6 \) are x = 3 and x = -9. These are the two values that satisfy the original equation.

Step-by-step solution

Understanding absolute value

An absolute value of a number can be thought of as its distance from zero. No matter if you go left or right from zero, distance is always positive. This means that absolute value of any number gives its magnitude without considering its sign. So, \(|n|\) is 'n' when 'n' is positive or zero and '-n' when 'n' is negative.

Convert into linear equations

The equation \( |x+3|=6 \) can be written as two separate equations considering the positive and negative results of the absolute value function. These two equations will be 'x + 3 = 6' and 'x + 3 = -6'.

Solve the first equation

Solving 'x + 3 = 6' for x, by subtracting 3 from both sides of the equation, gives us 'x = 3'.

Solve the second equation

Solving 'x + 3 = -6' for x, by subtracting 3 from both sides of the equation, gives us 'x = -9'.