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 equal to 3 end set

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

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

{x|x≥4}
start set x such that x is greater than or equal to 4 end set

Answer 1

To find the solution set, we need to solve both equations and inequalities provided:

1. Solve the equation \(3x - 2 = 7\):

\[ 3x - 2 = 7 \] Add 2 to both sides:

\[ 3x = 9 \] Now, divide by 3:

\[ x = 3 \]

2. Solve the inequality \(4x + 5 \leq 21\):

\[ 4x + 5 \leq 21 \] Subtract 5 from both sides:

\[ 4x \leq 16 \] Now, divide by 4:

\[ x \leq 4 \]

Now we combine the results from both parts.

• The equation gives us \(x = 3\).
• The inequality gives us all values \(x \leq 4\).

Since \(3\) is less than or equal to \(4\), the solution set that satisfies both is:

\[ {x | x \geq 3} \]

Hence, the final answer is:

Answer: \({x | x \geq 3}\)