Question

4/5x-3≤7/2
solve the inequality step by step

Answer 1

To solve the inequality \( \frac{4}{5}x - 3 \leq \frac{7}{2} \), follow these steps:

### Step 1: Isolate the term containing \( x \)
Add 3 to both sides of the inequality to isolate the term with \( x \).

\[
\frac{4}{5}x - 3 + 3 \leq \frac{7}{2} + 3
\]

This simplifies to:

\[
\frac{4}{5}x \leq \frac{7}{2} + 3
\]

### Step 2: Convert 3 to a fraction with the same denominator
To add \( \frac{7}{2} + 3 \), we convert 3 to a fraction with a denominator of 2:

\[
3 = \frac{6}{2}
\]

Now, we can add:

\[
\frac{7}{2} + \frac{6}{2} = \frac{7 + 6}{2} = \frac{13}{2}
\]

So the inequality now is:

\[
\frac{4}{5}x \leq \frac{13}{2}
\]

### Step 3: Eliminate the fraction on \( x \)
To eliminate the fraction, multiply both sides by \( \frac{5}{4} \). Note that since \( \frac{5}{4} \) is positive, the direction of the inequality does not change.

\[
x \leq \frac{13}{2} \cdot \frac{5}{4}
\]

### Step 4: Perform the multiplication
Calculate \( \frac{13}{2} \cdot \frac{5}{4} \):

\[
\frac{13 \cdot 5}{2 \cdot 4} = \frac{65}{8}
\]

So we have:

\[
x \leq \frac{65}{8}
\]

### Conclusion
The solution to the inequality \( \frac{4}{5}x - 3 \leq \frac{7}{2} \) is:

\[
x \leq \frac{65}{8}
\]

Or as a decimal, \( \frac{65}{8} = 8.125 \). Thus, you can write the solution as:

\[
x \leq 8.125
\]