Determine the solution set of 2x>−8 and −5x+7=12

Question

(1 point)
Responses

{−4}
start set negative 4 end set

{x|x>−4}
start set x such that x is greater than negative 4 end set

{−1}
start set negative 1 end set

{x|x>−1}

Answer 1

Let's solve the given inequalities and equations one by one.

1. Solve the inequality \(2x > -8\): \[ x > \frac{-8}{2} = -4 \] So, the solution set for this inequality is: \[ {x \mid x > -4} \]

2. Solve the equation \(-5x + 7 = 12\): \[ -5x = 12 - 7 \] \[ -5x = 5 \] \[ x = \frac{5}{-5} = -1 \] So, the solution to this equation is: \[ {-1} \]

Now, we can summarize the results:

• The solution set for the inequality \(2x > -8\) is \({x \mid x > -4}\).
• The solution to the equation \(-5x + 7 = 12\) is \({-1}\).

Since the problem asks for the solution to both parts, we focus on the broader solution set.

Among the provided options:

1. \({-4}\)
2. \({x \mid x > -4}\)
3. \({-1}\)
4. \({x \mid x > -1}\)

The relevant option that encompasses the solution from the first part (inequality) is: \({x \mid x > -4}\).

Therefore, the correct answer is: \({x \mid x > -4}\).