What is the solution set of 3x−2=7

Question

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: \({x | x \leq 4}\).