Question

What are the values for q that will make the equation true |4q+12|=4

Answer 1

Hi there! Solving the absolute value equation is like solving a quadratic equation.

$\large{ |x| = a \longrightarrow x = \pm a}$

$\large{ |x| = \begin{cases} x \: \: \: (x \geqslant 0) \\ - x \: \: \: (x < 0) \end{cases}}$

From the absolute equation:

$\large{ |4q + 12| = 4}$

Cancel the absolute symbol and write plus-minus of 4.

$\large{4q + 12 = \pm 4}$

Solve the equation for q-term.

$\large{4q = \begin{cases} 4 - 12 \\ - 4 - 12 \end{cases}} \\ \large{4q = \begin{cases} - 8 \\ - 16 \end{cases}} \\ \large{q = \begin{cases} - \frac{8}{4} \\ - \frac{16}{4} \end{cases}} \\ \large{q = \begin{cases} - 2 \\ - 4 \end{cases}}$

Hence, the value of q are -2,-4

Answer

• q = -2,-4