What is the solution set of x+1≥5 and 2x≥4

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 solve the inequalities \(x + 1 \geq 5\) and \(2x \geq 4\), we will solve each inequality separately.

1. For the first inequality \(x + 1 \geq 5\): \[ x + 1 \geq 5 \implies x \geq 5 - 1 \implies x \geq 4 \]

2. For the second inequality \(2x \geq 4\): \[ 2x \geq 4 \implies x \geq \frac{4}{2} \implies x \geq 2 \]

Next, we find the solution set that satisfies both inequalities:

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

The more restrictive condition is \(x \geq 4\), since any value that satisfies \(x \geq 4\) will also satisfy \(x \geq 2\).

Thus, the solution set for the system of inequalities is: \[ {x | x \geq 4} \] This corresponds to the response: \[ {x | x \geq 4} \]