# Solve |5 - 2y| + 3 = 8

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To solve `|5-2y|+3=8` , we need to use the absolute value function `|x|=x` if `x>=0` and `|x|=-x` if `x<0` .

This means that we are solving two equations, which are based on `5-2y>=0` which is the same as `-2y>=-5` or `y<=5/2` .

(1) if `y<=5/2` :

`5-2y+3=8`

`-2y=8-3-5`

`-2y=0`

`y=0` This is `<=5/2` so it is a valid solution.

(2) if `y>5/2`

`-(5-2y)+3=8`

`-5+2y+3=8`

`2y=8-3+5`

`2y=10`

`y=5`

Since this is `>5/2` it is also a valid solution.

**The two solutions are `y=0` and `y=5` .**

|5 - 2y| + 3 = 8

To solve this , first subtract 3 on both sides

By subtracting 3 on both sides , you should get

| 5 - 2y | = 5 now change this to

5 - 2y = 5 and 5 - 2y = -5

Now subtract 5 on both sides of both equation . By subtracting , you should get

-2y = 0 and -2y = -10 now divide by -2 on both sides of both equations .

By dividing , you should get

y = 0 and y = 5 which are your answers