Question

Solve for x: 12 (x – 4)| + 7 = 25.

Answer 1

Question:

Solve for x: $12|x-4|+7=25$. Fill in both values for x below. Write the greater value for x in the first column.

Answer:

$x=5.5$ and $x=2.5$ are the values for x.

Explanation:

The equation is $12|x-4|+7=25$

Subtracting both sides by 7,

$12|x-4|=18$

Dividing both sides by 12,

$|x-4|=1.5$

Now, we shall write the equation by removing modulus by adding plus and minus on the other side of the equation.

$x-4=1.5$ or $x-4=-1.5$

Solving the equation $x-4=1.5$, we get,

$\begin{aligned} x-4 &=1.5 \\ x &=1.5+4 \\ x &=5.5 \end{aligned}$     or      $\begin{aligned} x-4 &=-1.5 \\ x &=-1.5+4 \\ x &=2.5 \end{aligned}$

Thus, the solutions are $x=5.5$ and $x=2.5$