Question

In one shift working at a store, Irene earned more than $350 total. She made $160, plus x dollars in commission for each of 8 jackets she sold. How much could she have made for each jacket?
Write an inequality to represent the situation. Use x to represent the number of dollars she made for each jacket.
Great job!
You just wrote an inequality to represent the situation. Now solve the associated equation, 160 + 8x = 350, to find the boundary for the inequality. Show your work or solve on paper.
160 + 8x > 350
160+8x
=
350

x
=
Excellent!
Now figure out if the boundary, x = 23.75, is a solution to the inequality. Does x = 23.75 make the inequality true or false?
160 + 8x > 350

True

False

Answer 1

To represent the situation with an inequality, we can write:

\[ 160 + 8x > 350 \]

This means that Irene's total earnings (her base salary of $160 plus her commission for selling 8 jackets at \( x \) dollars each) are greater than $350.

Now, let's solve the associated equation to find the boundary for the inequality:

\[ 160 + 8x = 350 \]

To solve for \( x \):

1. Subtract 160 from both sides:
\[
8x = 350 - 160
\]
\[
8x = 190
\]

2. Divide both sides by 8:
\[
x = \frac{190}{8}
\]
\[
x = 23.75
\]

So, the boundary value we found is \( x = 23.75 \).

Now, let's check if this boundary makes the inequality true or false. We substitute \( x = 23.75 \) back into the inequality:

\[ 160 + 8(23.75) > 350 \]

Calculating the left side:

1. Multiply:
\[
8 \times 23.75 = 190
\]

2. Add:
\[
160 + 190 = 350
\]

So, we have:

\[ 350 > 350 \]

This statement is false since 350 is not greater than 350; it is equal.

Therefore, the answer to whether \( x = 23.75 \) makes the inequality true or false is:

**False**.