Question

Solve the inequality. Check your solutions.
7 y font size decreased by 10plus4less than25
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Part 1
The solution is y font size decreased by 10
▼
greater than or equals
less than
greater than
less than or equals
  
enter your response here.
​(Simplify your​ answer.)

Answer 1

Let's first rewrite the inequality according to the provided expression "7y - 10 + 4 < 25".

1. Combine like terms:
\[
7y - 6 < 25
\]

2. Now, add 6 to both sides:
\[
7y < 31
\]

3. Next, divide by 7:
\[
y < \frac{31}{7}
\]

Now we can simplify \(\frac{31}{7}\):
\[
\frac{31}{7} \approx 4.42857
\]

Thus, the solution to the inequality is:
\[
y < \frac{31}{7}
\]

Now let’s check the solution. We can test with a number less than \(\frac{31}{7}\), for example, \(y = 4\):

Evaluate \(7y - 10 + 4 < 25\):
\[
7(4) - 10 + 4 = 28 - 10 + 4 = 22 < 25
\]
This holds true.

Now, let’s test with a number greater than \(\frac{31}{7}\), for example, \(y = 5\):

Evaluate \(7y - 10 + 4 < 25\):
\[
7(5) - 10 + 4 = 35 - 10 + 4 = 29 < 25
\]
This does not hold true.

Thus, confirming that the solution \(y < \frac{31}{7}\) is correct.

**Final answer:**
\[
y < \frac{31}{7}
\]