Question:
Solve for x: [tex]$12|x-4|+7=25$[/tex]. Fill in both values for x below. Write the greater value for x in the first column.
Answer:
[tex]x=5.5[/tex] and [tex]x=2.5[/tex] are the values for x.
Explanation:
The equation is [tex]$12|x-4|+7=25$[/tex]
Subtracting both sides by 7,
[tex]$12|x-4|=18$[/tex]
Dividing both sides by 12,
[tex]$|x-4|=1.5$[/tex]
Now, we shall write the equation by removing modulus by adding plus and minus on the other side of the equation.
[tex]x-4=1.5[/tex] or [tex]x-4=-1.5[/tex]
Solving the equation [tex]x-4=1.5[/tex], we get,
[tex]$\begin{aligned} x-4 &=1.5 \\ x &=1.5+4 \\ x &=5.5 \end{aligned}$[/tex] or [tex]$\begin{aligned} x-4 &=-1.5 \\ x &=-1.5+4 \\ x &=2.5 \end{aligned}$[/tex]
Thus, the solutions are [tex]x=5.5[/tex] and [tex]x=2.5[/tex]
