What is the solution set of 3x−2=7

Question

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:

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