Math 7B. Pattering and Algebraic Reasoning. Spring25 Sample work

Question

Question 6
Consider the inequality.
5a + 18 < -27
Correctly order the steps used to solve the inequality.
Step 1
Step 2
Step 3
Finally, reverse the inequality, or Finally do not reverse the inequality
Solve for the solution set: 5a + 18 < - 27

Answer 1

To solve the inequality \( 5a + 18 < -27 \), we can break it down into ordered steps:

Steps to Solve

Step 1: Subtract 18 from both sides of the inequality.

\[ 5a + 18 - 18 < -27 - 18 \]

This simplifies to:

\[ 5a < -45 \]

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Step 2: Divide both sides by 5.

\[ \frac{5a}{5} < \frac{-45}{5} \]

This simplifies to:

\[ a < -9 \]

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Step 3: Finally, do not reverse the inequality. (When dividing or multiplying by a positive number, the direction of the inequality stays the same.)

Solution Set

Putting it all together, the solution set is:

\[ a < -9 \]

This means that any value of \( a \) that is less than -9 will satisfy the original inequality.