SOLUTION: Let g(x) = 5x − 7 + |x + 4|. Find all values of a which satisfy the equation g(a) = 4a + 3. (Enter your answers as a comma-separated list. If an answer does not exist

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Let g(x) = 5x − 7 + |x + 4|. Find all values of a which satisfy the equation g(a) = 4a + 3. (Enter your answers as a comma-separated list. If an answer does not exist      Log On


   

Question 707544: Let
g(x) = 5x − 7 + |x + 4|.
Find all values of a which satisfy the equation
g(a) = 4a + 3.
(Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Start by assigning x=a and equate it with the desired expression.
5a-7%2Babs%28a%2B4%29=4a%2B3
some steps,
abs%28a%2B4%29=4a-5a%2B3%2B7
abs%28a%2B4%29=-a%2B10

a+4 may be positive or negative.
If a%2B4%3E0 Then a%2B4=-a%2B10,
2a=14
a=7

If a%2B4%3C0 Then -%28a%2B4%29=-a%2B10,
-a-4=-a%2B10
-a-%28-a%29=10%2B4
0=14,
False statement.

Only answer is highlight%28a=7%29.