Sure! Let's solve the given inequality step-by-step to determine which phrase accurately describes the loan amount.
The inequality given is:
[tex]\[ 2x + \$15,000 \leq \$65,000 \][/tex]
1. Isolate the term with [tex]\( x \)[/tex]:
Subtract \[tex]$15,000 from both sides of the inequality to move the constant term on the left side to the right side.
\[ 2x \leq \$[/tex]65,000 - \[tex]$15,000 \]
2. Simplify the right side:
Subtracting the values on the right side:
\[ 2x \leq \$[/tex]50,000 \]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides of the inequality by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[ x \leq \frac{\$50,000}{2} \][/tex]
Simplifying the division:
[tex]\[ x \leq \$25,000 \][/tex]
So, to describe the loan amount based on our solution, [tex]\( x \)[/tex] should be less than or equal to \[tex]$25,000.
The most accurate phrase for the loan amount is:
"At most $[/tex]25,000"
