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

Question

Responses

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

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

{−4}left brace negative 4 right brace

{−1}

Answer 1

To solve the inequalities and equations given, we first handle each part separately.

1. Solve the inequality:

   \[ 2x > -8 \]

   Dividing both sides by 2:

   \[ x > -4 \]

2. Solve the equation:

   \[ -5x + 7 = 12 \]

   First, subtract 7 from both sides:

   \[ -5x = 5 \]

   Next, divide by -5 (remember that dividing or multiplying by a negative reverses the inequality):

   \[ x = -1 \]

Thus, we have:

• From the inequality, we have \( x > -4 \).
• From the equation, we have \( x = -1 \).

To find the solution set that includes both conditions, we note that the inequality \( x > -4 \) holds true for all \( x \) greater than -4, including \( x = -1 \). Therefore, within the context of the inequality, \( x = -1 \) is valid as it is greater than -4.

However, since the problem asks for solutions, we need to summarize our findings:

• The solution set for the inequality is \({ x | x > -4 }\).
• The equation yields a specific solution \(x = -1\).

Since the options given primarily consist of the solution for the inequality and specific points, the most appropriate response from the choices corresponding to the inequality is:

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

Final answer: {x | x > -4}