217k views
1 vote
|4x-8| =8 the equation has two solution find the sum if those two solution.

1 Answer

1 vote

This problem has an absolute value operator, this type of math operator receives a number as an input and outputs a positive value. This means that if we have an equation like "|x| = 3" it will have two possible solutions, because if x = -3 the result will be true and if x = 3 the result will also be true.

With this in mind let's solve the problem.


\begin{gathered} |4x\text = 8 \\ \end{gathered}

We need to create two equations. The first one is for the case where "4x -8" is greater than 0 and the second one if "4x -8" is less then 0.

For the first case we have:


\begin{gathered} 4x\text{ -8 = }8 \\ 4x\text{ = 8 + 8} \\ 4x\text{ = 16} \\ x=(16)/(4)\text{ =4} \end{gathered}

For the second case we have:


\begin{gathered} 4x\text{ - 8 = -8} \\ 4x\text{ = -8 +8} \\ 4x\text{ = 0} \\ x\text{ = 0} \end{gathered}

Therefore the two solutions are x = 0 and x = 4 and their sum is:


0+4\text{ = 4}

The answer to the problem is 4.

User Stolho
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.