What is the solution set of 2x+3≥7 and 2x≥8

Question

(1 point)
Responses

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

{x|x≤4}
start set x such that x is less than or equal to 4 end set

{x|x≥2}
start set x such that x is greater than or equal to 2 end set

{x|x≤2}
start set x such that x is less than or equal to 2 end set

Answer 1

To solve the inequalities \( 2x + 3 \geq 7 \) and \( 2x \geq 8 \), we can solve each one separately and then find their intersection.

1. First inequality:

   \( 2x + 3 \geq 7 \)

   Subtract 3 from both sides:

   \( 2x \geq 4 \)

   Divide both sides by 2:

   \( x \geq 2 \)

2. Second inequality:

   \( 2x \geq 8 \)

   Divide both sides by 2:

   \( x \geq 4 \)

Now we need to combine the results of the two inequalities:

• From the first inequality, we found \( x \geq 2 \).
• From the second inequality, we found \( x \geq 4 \).

The solution set that satisfies both inequalities is the more restrictive condition:

\( x \geq 4 \).

Thus, the solution set is:

\({ x \mid x \geq 4 }\).

So the correct response is:

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