Determine the solution set of 2x>−8 and −5x+7=12.(1 point)

Question

Responses

{x|x>−1}
left brace x vertical bar x greater than negative 1 right brace

{−1}
left brace negative 1 right brace

{−4}
left brace negative 4 right brace

{x|x>−4}
left brace x vertical bar x greater than negative 4 right brace

Answer 1

To solve the inequalities and equations given, let's break it down step-by-step.

1. Solve the inequality \(2x > -8\):

   • Divide both sides by 2: \[ x > -4 \]
   • This gives us the first part of our solution set: \[ {x | x > -4} \]

2. Solve the equation \(-5x + 7 = 12\):

   • Subtract 7 from both sides: \[ -5x = 5 \]
   • Divide both sides by -5: \[ x = -1 \]
   • This gives us the solution \(x = -1\).

Now, let's consider the solution set from both parts:

• From the inequality, we have \(x > -4\), which includes all values greater than -4.
• From the equation, we found a specific solution \(x = -1\).

The intersection of these two conditions is influenced by the inequality \(x > -4\). Thus, the \(x = -1\) lies within the set of values defined by \(x > -4\).

Therefore, the overall solution set based on the options provided is \( {x | x > -4} \).

The correct response is:

{x | x > −4}.