Question

Solve the inequality. Check your solutions.
5 f font size decreased by 10plus6greater than26
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Part 1
The solution is f font size decreased by 10
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greater than
less than or equals
less than
greater than or equals
  
enter your response here.

Answer 1

To solve the inequality given as "5f - 10 + 6 > 26," let's first combine the constants and then isolate \( f \).

### Step 1: Simplify the inequality
Combine the constants on the left side:
\[
5f - 10 + 6 > 26 \\
5f - 4 > 26
\]

### Step 2: Isolate \( f \)
Add 4 to both sides of the inequality:
\[
5f > 26 + 4 \\
5f > 30
\]

### Step 3: Divide by 5
Now divide both sides by 5:
\[
f > \frac{30}{5} \\
f > 6
\]

### Conclusion
The solution to the inequality is:
\[
f > 6
\]

### Check the solution
To confirm, we can test a value greater than 6, such as \( f = 7 \):
\[
5(7) - 10 + 6 > 26 \\
35 - 10 + 6 > 26 \\
31 > 26 \quad \text{(True)}
\]

Now, let's check a value less than or equal to 6, such as \( f = 6 \):
\[
5(6) - 10 + 6 > 26 \\
30 - 10 + 6 > 26 \\
26 > 26 \quad \text{(False)}
\]

Thus, the value \( f > 6 \) is indeed correct.

### Final answer
The solution is:
***f > 6***