SOLUTION: I have an absolute value question.... 5(5x+7)+2<=21...the parenthesis are the absolute value symbols....ive tried every step at different points in the equation, and i always en

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Question 504366: I have an absolute value question....
5(5x+7)+2<=21...the parenthesis are the absolute value symbols....ive tried every step at different points in the equation, and i always end up with the wrong answer....(-56/25,-26/25) i thought for sure was it but i was wrong....ive spent the last hour on this one. I know set the left side to -21 and commence the solving, isolate the absolue value and divide by 5 but every time i try, my math comes up short.
Found 2 solutions by stanbon, nic0le116:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
5|5x+7|+2 <= 21
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Subtract 2 from both sides:
5|5x+7| <= 19
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Divide by 5 to get:
|5x+7| <= 19/5
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-19/5 <= 5x+7 <= 19/5
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Multiply by 5 along the line:
-19 <= 25x + 35 <= 19
Subtract 35 along the line:
-54 <= 25x <= -16
Divide by 25 along the line:
-54/25 <= x <= -16/25
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Cheers,
Stan H.
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Answer by nic0le116(25) (Show Source):
You can put this solution on YOUR website!
We want to get the absolute value by itself
5(5x+7)+2<=21 (Subtract 2 from both sides)
5(5x+7) <=19 (Divide each side by 5)
5x+7 <=19/5 (Now we need to solve for both 19/5 and -19/5
-19/5<=5x+7<=19/5 (You can either set up two separate problems or build a 3 part problem.)
We need to get x alone.
Whatever you do to the middle to get x by itself, needs to be done to each side as well.
-19/5<=5x+7<=19/5 (subtract 7 from each side. Be sure to multiply 7/1 by 5 so you can get a common denominator and be able to subtract properly)
-54/5<=5x<=-16/5 (Now we need to divide each side by 5 to get x alone. Remember to divide by fractions, take the reciprocal and multiply- So we will be multiplying the left and right side by 1/5)
-54/25<=x<=-16/25
X is greater than or equal to -54/25
X is less than or equal to -16/25