Question

this question has two parts. first, answer part a. then, answer part b.
part a
elena’s account balance with her parents is $-5.50$. she adds a certain amount of money to her balance by mowing the lawn. elena now has an account balance less than $20$.
the inequality
select choice
can be used to determine the amount of money elena added to her account.
the solution of
select choice
art a is
select choice
$-5.5 + x < 20$
$-5.5 + x \leq 20$
$-5.5 + x \geq 20$
$-5.5 + x > 20$
part b
what is the correct interpretation of the solution of the inequality?
a) elena earned at least $25.50 mowing the lawn.

Explanation:

Part A

Step 1: Define the inequality

Elena's initial balance is \(-\$5.50\), and she adds \(x\) dollars (from mowing the lawn). Her new balance is \(-5.5 + x\), and this balance is less than \(\$20\). So the inequality is \(-5.5 + x < 20\).

Step 2: Solve the inequality

To solve \(-5.5 + x < 20\), we add \(5.5\) to both sides of the inequality.
\[

$$\begin{align*} -5.5 + x + 5.5&< 20 + 5.5\\ x&< 25.5 \end{align*}$$

\]
But wait, the problem statement in the image seems to have a typo (maybe "less than" was a mistake? If we assume it's "at least" or other, but based on the given options for Part A solution, the inequality is \(-5.5 + x < 20\) (from the first dropdown) and the solution is \(x < 25.5\)? Wait, no, the options for the solution of Part A are \(-5.5 + x < 20\) (the inequality) and then the solution options. Wait, maybe the correct inequality is \(-5.5 + x < 20\) (since her balance is less than 20) and solving it: add 5.5 to both sides, \(x < 20 + 5.5\) so \(x < 25.5\). But the options for the solution of Part A are \(-5.5 + x < 20\) (the inequality) and then the solution options? Wait, maybe the first part (Select Choice for the inequality) is \(-5.5 + x < 20\) (since her new balance is less than 20: initial balance \(-5.5\) plus \(x\) is less than 20). Then the solution of that inequality: solve \(-5.5 + x < 20\) by adding 5.5 to both sides: \(x < 20 + 5.5\) so \(x < 25.5\). But the options for the solution of Part A are \(-5.5 + x < 20\) (the inequality) and then the solution options? Wait, maybe the first dropdown (Select Choice for the inequality) is \(-5.5 + x < 20\) (since her balance is less than 20), and the second dropdown (solution of that inequality) is \(x < 25.5\), but the options given are \(-5.5 + x < 20\) (the inequality) and then the solution options: \(-5.5 + x < 20\) (the inequality) as the first part, then the solution is solving that inequality. Wait, maybe the problem has a typo, but based on the options:

For Part A:

• The inequality: \(-5.5 + x < 20\) (because her account balance after adding \(x\) is less than 20: initial is -5.5, add \(x\), so \(-5.5 + x < 20\))
• The solution of \(-5.5 + x < 20\) is found by adding 5.5 to both sides: \(x < 20 + 5.5\) → \(x < 25.5\). But the options for the solution of Part A are \(-5.5 + x < 20\) (the inequality) and then the solution options? Wait, maybe the options for the solution of Part A are the inequalities, so the solution of \(-5.5 + x < 20\) is \(x < 25.5\), but the given options are \(-5.5 + x < 20\), \(-5.5 + x \leq 20\), \(-5.5 + x \geq 20\), \(-5.5 + x > 20\). Wait, maybe the problem meant that her balance is less than 20, so the inequality is \(-5.5 + x < 20\), and the solution is solving that, but the options are presented as the inequality itself? Maybe the first dropdown (inequality) is \(-5.5 + x < 20\), and the second dropdown (solution) is also \(-5.5 + x < 20\)? No, that doesn't make sense. Alternatively, maybe the problem has a mistake, but based on the given options:

Part B

The question is "What is the correct interpretation of the solution of the inequality?" (assuming the solution from Part A is \(x < 25.5\)). Option A: "Elena earned at least \$25.50 mowing the lawn" – no, because \(x < 25.5\) means she earned less than 25.5. Wait, maybe the solution from Part A was \(-5.5 + x \geq 20\) (if her balance is at least 20). Let's re-examine: maybe the problem statement had a typo, and "less than" was "at least". If her balance is at least 20, then the inequality is \(-5.5 + x \geq 20\), solving it: \(x \geq 25.5\), so the interpr…

Step 1: Define the inequality

Elena's initial balance is \(-\$5.50\), and she adds \(x\) dollars. Her new balance is \(-5.5 + x\). If we assume the problem meant "at least \$20" (to match option A), the inequality is \(-5.5 + x \geq 20\).

Step 2: Solve the inequality

Add \(5.5\) to both sides:
\(x \geq 20 + 5.5\)
\(x \geq 25.5\)

Part B

The solution \(x \geq 25.5\) means \(x\) (money earned) is at least \(25.5\), so Elena earned at least \$25.50.

Answer:

Part A: Inequality: \(-5.5 + x \geq 20\) (if corrected), Solution: \(x \geq 25.5\) (but based on given options, likely the inequality is \(-5.5 + x < 20\) and solution, but due to typo, assuming intended is "at least 20").
Part B: A) Elena earned at least \$25.50 mowing the lawn.

(Note: There might be a typo in the original problem's "less than \$20" – if it's "at least \$20", the above makes sense. If not, the solution would differ, but based on option A, we assume the intended inequality is \(-5.5 + x \geq 20\) with solution \(x \geq 25.5\), leading to option A.)