Question

What is the solution set of 3x−2=7
and 4x+5<21
(1 point)
Responses

{x|x≥3}
start set x such that x is greater than or equal to 3 end set

{x|x=3}
start set x such that x is equal to 3 end set

{x|x=4}
start set x such that x is equal to 4 end set

{x|x≥4}

Answer 1

To solve the two given equations and inequalities:

1. **Solve the equation \(3x - 2 = 7\)**:
\[
3x - 2 = 7
\]
Add 2 to both sides:
\[
3x = 7 + 2
\]
\[
3x = 9
\]
Divide both sides by 3:
\[
x = 3
\]

2. **Solve the inequality \(4x + 5 < 21\)**:
\[
4x + 5 < 21
\]
Subtract 5 from both sides:
\[
4x < 21 - 5
\]
\[
4x < 16
\]
Divide both sides by 4:
\[
x < 4
\]

Now we summarize the solutions:

- From the first part, \(x = 3\).
- From the second part, \(x < 4\).

Considering these results together, the solution set includes values of \(x\) that are at least 3 and less than 4. Thus, the solution set can be expressed as:

\[
\{x \mid 3 \leq x < 4\}
\]

If we analyze the provided responses, the most appropriate answer based on the context is:

\(\{x \mid x \geq 3\}\) since it allows \(x = 3\) and anything above it.

Thus, the solution that fits best in the context of your query is:

\(\{x \mid x \geq 3\}\)