Answer:
|-4a+10|=2 when a = 2 or a = 3.
Step-by-step explanation:
Your problem is a modular function problem
Modular function
The modulus of a value is the distance of the value to the origin.
It is quite helpful to start this kind of problem from a simple example.
|a| = b is if a = b or if a = -b. |x| = 2 if x = 2 or if x = -2. In both cases, the distance to the origin is 2.
So in your question, we have:
a = -4a + 10
b = 2
Now we have to apply both cases.
Solution 1: |a| = b if a = b
a = b
-4a + 10 = 2
-4a = -8 *(-1)
4a = 8
[tex]a = \frac{8}{4}[/tex]
a = 2
Solution 1: |a| = b if a = -b
a = -b
-4a + 10 = -2
-4a = -12 *(-1)
4a = 12
[tex]a = \frac{12}{4}[/tex]
a = 3
So, |-4a+10|=2 when a = 2 or a = 3.
