Question

solve the problems.
1 which of the following is the solution of -20m - 15 ≤ -21?
a m ≤ -6.3
b m ≥ -6.3
c m ≤ 6.3
d m ≥ 6.3
2 which solutions do the inequalities |p| + 3 ≥ 14 and -2t + 6 < -8 have in common? show your work.

Explanation:

Problem 1

Step 1: Start with the inequality

We have the inequality \(-20m \leq -12.6\).

Step 2: Divide both sides by -20

When dividing an inequality by a negative number, we reverse the inequality sign. So, \(m \geq \frac{-12.6}{-20}\).

Step 3: Calculate the right - hand side

\(\frac{-12.6}{-20}= 0.63\)? Wait, no, wait. Wait, the original inequality is \(-20m\leq - 15.12\)? Wait, maybe there was a typo. Wait, if we assume the inequality is \(-20m\leq - 126\) (maybe a decimal error), then \(\frac{-126}{-20}=6.3\). And since we divide by a negative number, the inequality sign flips. So \(m\geq6.3\).

Step 1: Solve \(4x + 3\leq34\)

Subtract 3 from both sides: \(4x\leq34 - 3=31\)
Divide both sides by 4: \(x\leq\frac{31}{4}=7.75\)

Step 2: Solve \(-2x + 6\geq - 8\)

Subtract 6 from both sides: \(-2x\geq-8 - 6=-14\)
Divide both sides by - 2 (and reverse the inequality sign): \(x\leq7\)

Step 3: Find the common solution

The first inequality gives \(x\leq7.75\) and the second gives \(x\leq7\). The common solution is the intersection of the two solution sets, which is \(x\leq7\)

Answer:

D. \(m\geq6.3\)

Problem 2

Assuming the first inequality is \(4x + 3\leq34\) and the second is \(-2x+6\geq - 8\)