Determine the solution set of 2x>−8 and −5x+7=12 .(1 point) Responses {x|x>−4} left brace x vertical bar x greater than negative 4 right brace {−4} left brace negative 4 right brace {−1} left brace negative 1 right brace {x|x>−1}

Answer 1

To determine the solution set for the inequalities and equations given, we need to solve each part individually.

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

   Divide both sides by 2: \[ x > -4 \]

   This means that the solution set is \( { x \mid x > -4 } \).

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

   First, we subtract 7 from both sides: \[ -5x = 12 - 7 \] \[ -5x = 5 \]

   Next, divide both sides by -5: \[ x = -1 \]

   This gives us the solution \( {-1} \).

Now we combine the solution sets:

• From the inequality \(2x > -8\), we have \( { x \mid x > -4 } \).
• From the equation \(-5x + 7 = 12\), we have \( {-1} \).

Both solutions are valid in their own contexts. However, since \(-1\) does not contradict the inequality \(x > -4\), we can consider both parts together.

Thus, the overall range of solutions can be expressed as combining \( { x \mid x > -4 } \) and the specific point \( {-1} \).

The best representation from the provided response options for the solution of the inequality \(x > -4\) is:

\[ { x \mid x > -4 } \]

Thus, the final answer is:

{x | x > -4} (left brace x vertical bar x greater than negative 4 right brace)