Solve for p. ∣−3p∣>6Write a compound inequality like 1<x<3 or like x<1 or x>3. Use integers, proper fractions, or improper fractions in simplest form.______
Q. Solve for p. ∣−3p∣>6Write a compound inequality like 1<x<3 or like x<1 or x>3. Use integers, proper fractions, or improper fractions in simplest form.______
Absolute Value Inequality: We have the inequality: ∣−3p∣>6First, we solve for ∣−3p∣.∣−3p∣>6 means that the absolute value of −3p is greater than 6.
Splitting Inequality: Since the absolute value of a number is always non-negative, we can split the inequality into two separate inequalities without the absolute value:−3p>6 or −3p<−6
Solving First Inequality: Now we solve each inequality separately. Starting with the first one:−3p>6Divide both sides by −3 to isolate p. Remember that dividing by a negative number reverses the inequality sign:p<−2
Solving Second Inequality: Next, we solve the second inequality:−3p<−6Again, divide both sides by −3, and reverse the inequality sign:p>2
Combining Solutions: Combining both parts of the solution, we get the compound inequality:p<−2 or p>2This is the final answer in the form of a compound inequality.
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