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

Question

(1 point)
Responses

{−1}
start set negative 1 end set

{−4}
start set negative 4 end set

{x|x>−1}
start set x such that x is greater than negative 1 end set

{x|x>−4}

Answer 1

To solve the given inequalities and equation:

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

   Divide both sides by 2: \[ x > -4 \] So, this gives us the solution set: \[ {x | x > -4} \]

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

   Subtract 7 from both sides: \[ -5x = 5 \] Now divide by -5: \[ x = -1 \]

Now we have two results:

• The inequality gives \(x > -4\).
• The equation gives the specific solution \(x = -1\).

Since \(-1\) is a number that is greater than \(-4\), it satisfies the condition from the inequality.

Now, considering the options provided:

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

The solution set based on the inequality \(x > -4\) is represented as: \({x | x > -4}\).

Though \(-1\) is a solution from the equation, the overall solution set that encompasses the inequality is broader.

Thus, the best answer from the options given is: \({x | x > -4}\).