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QuestionSolve the equation ∣5a+8∣=∣5a−6∣|5a + 8| = |5a - 6| and find the solution set: A. (Type answer) B. ∅\varnothing.

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, |x| = x if x is positive or zero, and |x| = -x if x is negative. . We are solving for the variable 'a' in the equation |5a +8| = |5a -6|.

STEP 2

The equation |5a +8| = |5a -6| can be split into two separate equations, because the absolute value of a number can be either positive or negative. The two equations are1.5a +8 =5a -62.5a +8 = -(5a -6)

STEP 3

Let's solve the first equation,5a +8 =5a -6.
Subtract5a from both sides of the equation to isolate the variable 'a'.
5a−5a+8=5a−5a−65a -5a +8 =5a -5a -6

STEP 4

implify the equation.
8=−68 = -6

STEP 5

The equation8 = - is not true, so there are no solutions from the first equation.

STEP 6

Now, let's solve the second equation,5a +8 = -(5a -6).
istribute the negative sign on the right side of the equation.
5a+8=−5a+65a +8 = -5a +6

STEP 7

Add5a to both sides of the equation to isolate the variable 'a'.
5a+5a+=−5a+5a+65a +5a + = -5a +5a +6

STEP 8

implify the equation.
10a+8=610a +8 =6

STEP 9

Subtract8 from both sides of the equation to isolate the variable 'a'.
a+8−8=6−8a +8 -8 =6 -8

STEP 10

implify the equation.
10a=−210a = -2

STEP 11

Divide both sides of the equation by10 to solve for 'a'.
a=−/10a = - /10

STEP 12

implify the fraction to get the solution for 'a'.
a=−/5a = -/5So, the solution set is -/5.

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