Answer:
solving the inequality [tex]|-2-10p|+2<70[/tex] we get [tex]\mathbf{-7 < p < \frac{33}{5}}[/tex]
Step-by-step explanation:
We need to solve the inequality
[tex]|-2-10p|+2<70[/tex]
Step 1: Subtract 2 from both sides
[tex]|-2-10p|+2-2<70-2\\|-2-10p|<68[/tex]
Step 2: Using the rule |u| < a then -a < u < a
[tex]-68<-2-10p<68[/tex]
Step 3: Solving:
[tex]-2-10p >-68 \ or \ -2-10p < 68\\-10p >-68+2 \ or \ -10p < 68+2\\-10p >-66 \ or \ -10p < 70[/tex]
Step 4: Divide both sides by -10, the inequalities will be reversed
[tex]\frac{-10p}{-10}<\frac{-66}{-10} \ or \ \frac{-10p}{-10}>\frac{70}{-10}\\p<\frac{33}{5} \ or \ p>-7[/tex]
Step 5: Combining the terms
[tex]-7 < p < \frac{33}{5}[/tex]
So, solving the inequality [tex]|-2-10p|+2<70[/tex] we get [tex]\mathbf{-7 < p < \frac{33}{5}}[/tex]
