Question

1. a teacher writes the inequality ( x + 5 < -12 ) on the board. vincent incorrectly solves the inequality and obtains ( x < -2 ) as the solution.

a. what was vincent’s likely error?
b. what is the correct solution?

1. higher order thinking a student needs three pieces of wire for a science project. the second piece must be 3 times as long as the first. the third piece must be twice as long as the second. the student has 350 inches of wire to make the three pieces. let ( x ) be the length of the first piece of wire.

a. look for relationships write an inequality that models this situation.
b. what are the possible lengths of the shortest piece of wire?
solve the inequality.

1. ( -\frac{q}{100} leq 6 )
2. luna is buying food for a dinner party. she is going to buy 2 key lime pies that cost $8.99 each. shrimp costs $8.50 a pound. she needs to spend less than $45 total. write an inequality to represent the situation. how many pounds of shrimp can she buy? round to the nearest whole pound.
3. on the first of the month, the balance of amelia’s saving account was $60. she plans to deposit $20 each week until she has at least $475 saved. write and solve the situation. how many deposits does she need to make to reach her goal?

Explanation:

Let's solve problem 9: Solve the inequality \(\boldsymbol{-\frac{q}{100} \leq 6}\)

Step 1: Multiply both sides by -100

To isolate \( q \), we multiply both sides of the inequality by \(-100\). Remember that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign flips.

\[
-\frac{q}{100} \times (-100) \geq 6 \times (-100)
\]

Step 2: Simplify both sides

Simplify the left side: \(-\frac{q}{100} \times (-100) = q\)

Simplify the right side: \(6 \times (-100) = -600\)

So we get \( q \geq -600 \)

Answer:

The solution to the inequality \(-\frac{q}{100} \leq 6\) is \( q \geq -600 \)