Question

consider the inequality
-4x-5<31
correctly order the steps used to solve the inequality
step 1:
step 2:
step 3:
a. add 4 to both sides of the inequality
b. add 5 to both sides of the inequality
c. subtract 5 from both sides of the inequality
d.multiply by -4 on both sides of the inequality
e. divide by -4 on both sides of the inequality
f. multply by -5 on both sides of the inequality
g. finally reverse the inequality
h. finally do not reverse the inequality

Answer 1

To solve the inequality \(-4x - 5 < 31\), you can correctly order the steps as follows:

**Step 1: c. subtract 5 from both sides of the inequality**
This gives you:
\(-4x < 31 + 5\)
\(-4x < 36\)

**Step 2: a. add 4 to both sides of the inequality**
This step is incorrect for isolating \(x\), so we will skip it. Instead, proceed directly to step 3.

**Step 3: e. divide by -4 on both sides of the inequality**
Remember to reverse the inequality when you divide by a negative number:
\(x > \frac{36}{-4}\)
\(x > -9\)

**Step 4: g. finally reverse the inequality**
This is applied when dividing by the negative number \(-4\).

So, the three main steps involved in solving the inequality can be summarized as:

**Step 1:** c
**Step 2:** e
**Step 3:** g

Final answer:
**Step 1:** c
**Step 2:** e
**Step 3:** g