skills

To complete this question, you need to be familiar with the modulus function and how to eliminate it to solve equations.

Question

Solve the equation below, giving your answer in terms of $a$ $$ |4a - 12x| = 2a $$

answer --- press button to toggle display

The answers are $x = \frac{1}{2}a$ and $x = \frac{1}{6}a$

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To solve the equation $|4a - 12x| =2a$, we need to consider two equations

- The equation $+(4a -12x) = 2a$
- The equation $-(4a - 12x) = 2a$

Consider the first equation $$\begin{array}{rcl} (4a -12x) &=& 2a \\ 2a &=& 12x \\ x &=& \frac{1}{6}a \end{array} $$ The second question yields $$\begin{array}{rcl} -(4a -12x) &=& 2a \\ -4a + 12x &=& 2a \\ 12x &=& 6a \\ x &=& \frac{1}{2}a \end{array} $$ Note that these distinct solutions exist only if $a\gt 0$. If $a=0$, then we have only the solution $x=0$. If $a\lt 0$ then the equation has no solutions.