# math

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solve the given inequality and graph its solution on the number line

2-x/3less than or eqaul to (</) 3-2x/5

lxl less than or equal to 5

2 is less than or eqaul to lx-6l less than or equal to 5

• math -

1.

2 - x/3 < 3 - 2x/5
multiply by 15, the LCD
30 - 5x ≤ 45 - 6x
6x - 5x ≤ 45-30
x ≤ 15

2.

|x| ≤ 5
x ≤ 5 AND -x≤5
x≤5 AND x≥-5
in short notation: -5 ≤ x ≤ 5

3.

2 ≤ |x-6| ≤ 5

case1: 2 ≤ x-6≤ 5
8 ≤ x ≤ 11

case2:
2 ≤ -x+6≤ 5
-4 ≤ -x ≤ -1
4 ≥ x ≥ 1 or
1 ≤ x ≤ 4

so 8 ≤ x ≤ 11 OR 1 ≤ x ≤ 4

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