Question

What is the solution set of 2x+3≥7 and 2x≥8 (1 point) Responses {x|x≥2} start set x such that x is greater 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≤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

Answer 1

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

1. For the first inequality: \[ 2x + 3 \geq 7 \] Subtract 3 from both sides: \[ 2x \geq 4 \] Now, divide both sides by 2: \[ x \geq 2 \]

2. For the second inequality: \[ 2x \geq 8 \] Divide both sides by 2: \[ x \geq 4 \]

Now, we need to combine the solutions of both inequalities. The first inequality gives \(x \geq 2\) and the second yields \(x \geq 4\). The more restrictive condition is \(x \geq 4\).

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

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