Question

solve.

5a + 4

=

6a - 10

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is
(simplify your answer. type an integer or a fraction. use a comma to separate answers as needed.)
b. the solution is all real numbers.
c. the solution is the empty set.

Explanation:

Step1: Set up two equations

When \(|5a + 4|=|6a - 10|\), we have two cases:
Case 1: \(5a + 4=6a - 10\)
Case 2: \(5a + 4=-(6a - 10)\)

Step2: Solve Case 1

\(5a + 4=6a - 10\)
Subtract \(5a\) from both sides: \(4=a - 10\)
Add 10 to both sides: \(a = 14\)

Step3: Solve Case 2

\(5a + 4=-(6a - 10)\)
Simplify the right side: \(5a + 4=-6a + 10\)
Add \(6a\) to both sides: \(11a + 4 = 10\)
Subtract 4 from both sides: \(11a=6\)
Divide by 11: \(a=\frac{6}{11}\)

Answer:

The solution set is \(14,\frac{6}{11}\) (corresponding to option A)