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

Question

(1 point)
Responses

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

{x|x≥4}
start set x such that x is greater 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≤4}

Answer 1

To find the solution set for the inequalities \( 2x + 3 \geq 7 \) and \( 2x \geq 8 \), we will solve each inequality separately.

1. Solve \( 2x + 3 \geq 7 \): \[ 2x + 3 \geq 7 \ 2x \geq 7 - 3 \ 2x \geq 4 \ x \geq \frac{4}{2} \ x \geq 2 \]

2. Solve \( 2x \geq 8 \): \[ 2x \geq 8 \ x \geq \frac{8}{2} \ x \geq 4 \]

Now we combine the results from both inequalities:

• The first inequality gives us \( x \geq 2 \).
• The second inequality gives us \( x \geq 4 \).

The solution set for both conditions must satisfy the stricter of the two conditions, which is \( x \geq 4 \).

Thus, the solution set is: \[ { x \mid x \geq 4 } \]

So the correct answer is:

• {x|x≥4}