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

(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}

1 answer

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: \[ {x | x \geq 4} \]

Similar Questions
  1. 2. Determine the solution set of −3x+7=10or 3x−9=0 (1 point) Responses {−1} start set negative 1 end set {3} start set 3
    1. answers icon 1 answer
  2. Determine the solution set of −3x+7=10 or 3x−9=0(1 point) Responses The solution set is null The solution set is null
    1. answers icon 1 answer
  3. Determine the solution set of −3x+7=10 or 3x−9=0(1 point) Responses {−1,3} start set negative 1 comma 3 end set The
    1. answers icon 1 answer
  4. Solve the following system of equations using the elimination method.0.1x+0.3y=0.9 , 0.1x−0.3y=0.2 (1 point) Responses There
    1. answers icon 1 answer
more similar questions