Question
Asked Dec 18, 2019
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solve the equation or inequality. Write the solution set to the inequalities in interval notation.

|3x − 5| = |2x + 1|

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Expert Answer

Step 1

Given equation is,

|3x − 5| = |2x + 1|

Consider (3x – 5) = 0

3x = 5

x = 5/3

Consider (2x +1) = 0

2x = -1

x = -1/2

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and x2=. Then the intervals are x < 2° Sx<-

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Step 2

For each absolutes form the below table,

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1 5 Sx<- 3 3 |3x 5| |2x +1|

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Step 3

Hence,

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For x <- 2 |3x - 5| is negative and |2x + 1| is also negative. Then, -(3x- 5) =-(2x+1) Зх -5 %3D 2х +1 Зх - 2х %3D 1+5 x = 6 1 But, x< Hence, there is no solution in this interval.

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