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Solve the inequality and show step by step

|-2-10p|+2<70

User Lewurm
by
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1 Answer

3 votes

Answer:

solving the inequality
|-2-10p|+2<70 we get
\mathbf{-7 < p < (33)/(5)}

Explanation:

We need to solve the inequality


|-2-10p|+2<70

Step 1: Subtract 2 from both sides


|-2-10p|+2-2<70-2\\|-2-10p|<68

Step 2: Using the rule |u| < a then -a < u < a


-68<-2-10p<68

Step 3: Solving:


-2-10p >-68 \ or \ -2-10p < 68\\-10p >-68+2 \ or \ -10p < 68+2\\-10p >-66 \ or \ -10p < 70

Step 4: Divide both sides by -10, the inequalities will be reversed


(-10p)/(-10)<(-66)/(-10) \ or \ (-10p)/(-10)>(70)/(-10)\\p<(33)/(5) \ or \ p>-7

Step 5: Combining the terms


-7 < p < (33)/(5)

So, solving the inequality
|-2-10p|+2<70 we get
\mathbf{-7 < p < (33)/(5)}

User Oleg Barshay
by
8.4k points

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