SOLUTION: Please help me answer this: abs(4a+7)<13 I got -5<a<3/7. I am not sure if this is right.

Question 155517: Please help me answer this: abs(4a+7)<13
I got -5
Found 3 solutions by Earlsdon, stanbon, Adam:
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Solve for a:
Remove the absolute-value bars and write the two resulting inequalities:
and Now solve each one of these inequalities.
Subtract 7 from both sides.
Divide both sides by 4.
or
-------------
Subtract 7 from both sides.
Divide both sides by 4.

Notice that you get two answers when solving inequalities such as this.

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
abs(4a+7)<13
-----------------
Solve the EQUALITY:
4a+7 = 13 or 4a+7 = -13
a = 3/2 or a = -5
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Draw a Number line and plot the points a = -5 and 3/2
------------------------
Check a value from each of resulting three intervals in the INEQUALITY
to see where the solution set is.
------------------------
Let a = -6, then |4*-6+7| <13; false, so no solutions in (-inf,-5)
------------
Let a = 0, then |4*0+7} < 13 ; true, so solutions in (-5,3/2)
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Let a = 2 then |4*2+7| < 13 ; false, so no solutions in (3/2,+inf)
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Final Answer: -5 < a < 3/2
=================================
Cheers,
Stan H.

Answer by Adam(64)   (Show Source): You can put this solution on YOUR website!
Actually, it is right only partially. 3/7 is wrong, let me show you why.
we start with
there are two cases, expression under absolute value (4a+7) can be negative, or nonnegative. If it is nonnegative there is no change to the equation, thus we can rewrite it as and solve:
//-7
//:4
=>
Cheers,
Adam
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