SOLUTION: can you please help me to identify the solution to the inequality |5-3x|+3 less than or equal to 7 thank you

Question 201753: can you please help me to identify the solution to the inequality |5-3x|+3 less than or equal to 7
thank you
Found 2 solutions by solver91311, RAY100:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First add -3 to both sides:

Now divide it into two inequalities (remember to reverse the sense of the inequality when multiplying by a negative number):

John

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
[ 5-3x] +3 <= 7
.
[5-3x] <= 4
.
(5-3x) <= +4,,,,,,,(5-3x) >= -4
.
-3x <= -1,,,,,,,,,,,,-3x >= -9
.
x >= 1/3,,,,,,,,,,,,,,,x <= 3
.
check
x less than 1/3,,,test point = 0, [5] +3 <= 7,,,8<=7,,,not true
.
x >=1/3,and x<=3,,test point = 2,,[5-6] +3 <= 7,,4<=7,,,,ok
.
x>3,,,,,test point = 4,,,[ 5-12] +3 <=7,,7+3<=7,,,,not true
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