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 less than or equal to 2 end set

{x|x≥2}

Answer 1

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

1. Solve \(2x + 3 \geq 7\): \[ 2x + 3 \geq 7 \] Subtract 3 from both sides: \[ 2x \geq 4 \] Divide by 2: \[ x \geq 2 \]

2. Solve \(2x \geq 8\): \[ 2x \geq 8 \] Divide by 2: \[ x \geq 4 \]

Now, we need to find the solution set that satisfies both inequalities. The solution for \(2x + 3 \geq 7\) gives us \(x \geq 2\), and the solution for \(2x \geq 8\) gives us \(x \geq 4\).

The more restrictive condition is \(x \geq 4\), since it includes all values that satisfy \(x \geq 2\).

Thus, the solution set for the given inequalities is: \[ {x ,|, x \geq 4} \]

Therefore, the correct response is: {x|x≥4}