Question

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

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

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

{x|x≤3}
start set x such that x is less than or equal to 3 end set

{x|x≤4}

Answer 1

To solve the equations and inequalities, let's do this step by step:

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

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

Now, we combine the results from both parts:

- The equation gives \(x = 3\), and the inequality gives \(x \leq 4\).
- Therefore, the solution set must satisfy both conditions.

Since \(x = 3\) is included in the solution of the inequality \(x \leq 4\), the most general solution set that includes the solution to the equation is:
\[
\{x | x \leq 4\}
\]

Thus, the correct response is:
\(\{x | x \leq 4\}\).