Question

The solution set of inequation|2x-3|<|x+2| is​

Answer 1

Answer:

x=1/3" or " x=5

Explanation:

There are 2 possible solutions to the equation.

2x-3=color(red)(+-)(x+2)

color(blue)"first solution"

2x-3=x+2

"subtract x from both sides."

2x-x-3=cancel(x)cancel(-x)+2

rArrx-3=2

"add 3 to both sides."

xcancel(-3)cancel(+3)=2+3

rArrx=5

color(blue)"second solution"

2x-3=-x-2

rArr3x=1

rArr x=1/3

color(blue)"As a check"

Substitute these values into the equation and if the left side is equal to the right side then they are the solutions.

"left side "=|(2xx5)-3|=|7|=7

"right side "=|5+2|=|7|=7

"left side "=|2/3-3|=|-2 1/3|=2 1/3

"right side "=|1/3+2|=|2 1/3|=2 1/3

rArrx=1/3" or " x=5" are the solutions"

Step-by-step explanation:

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