Question

StartFraction 5 left parenthesis x minus 6 right parenthesis Over 3 EndFraction
greater than or equalsStartFraction 3 x Over 5 EndFraction
minus15
The solution as an inequality is
  
enter your response here.

Answer 1

To solve the inequality

\[
\frac{5(x - 6)}{3} \geq \frac{3x}{5} - 15,
\]

we will first clear the fractions by finding a common multiple. The common denominator for 3 and 5 is 15.

Multiply every term by 15:

\[
15 \cdot \frac{5(x - 6)}{3} \geq 15 \cdot \left( \frac{3x}{5} - 15 \right)
\]

This simplifies to:

\[
5 \cdot 5(x - 6) \geq 3 \cdot 15x - 15 \cdot 15.
\]

Simplifying further, we get:

\[
25(x - 6) \geq 45x - 225.
\]

Distributing \(25\) on the left side,

\[
25x - 150 \geq 45x - 225.
\]

Now, we can rearrange the terms to isolate \(x\). Move \(25x\) to the right side and \(-225\) to the left side:

\[
-150 + 225 \geq 45x - 25x.
\]

This simplifies to:

\[
75 \geq 20x.
\]

Now, divide both sides by \(20\):

\[
\frac{75}{20} \geq x.
\]

This simplifies to:

\[
\frac{15}{4} \geq x,
\]

or equivalently:

\[
x \leq \frac{15}{4}.
\]

Thus, the solution to the inequality is:

\[
x \leq \frac{15}{4}.
\]