SOLUTION: Solve the inequality and write the solution in interval notation: 3|7a+1|-5≥ 76

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Question 1133398: Solve the inequality and write the solution in interval notation:
3|7a+1|-5≥ 76

Found 2 solutions by MathLover1, addingup:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3abs%287a%2B1%29-5%3E=76

3abs%287a%2B1%29%3E=76+%2B5
3abs%287a%2B1%29%3E=81
abs%287a%2B1%29%3E=81%2F3
abs%287a%2B1%29%3E=27
solutions:
=>7a%2B1%3E=27=>7a%3E=27-1=>7a%3E=26=>a%3E=26%2F7
=>-%287a%2B1%29%3E=27=>-7a-1%3E=27=>-28%3E=7a=>a%3C=-28%2F7=>a%3C=-4

the solution in interval notation:
(-infinity, -4] U [26%2F7, infinity)
number line:
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Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for a:
3|7a+1|-5 ≥ 76
3|7a+1| ≥ 81
|7a+1|/3 ≥ 81/3
|7a+1| ≥ 27
7a+1 ≥ 27 or 7a+1 ≤ −27
7a ≥ 26 or 7a ≤ −28
a ≥ 26/7 or a ≤ −4