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

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

{−1}
left brace negative 1 right brace

{−4}

Answer 1

To solve the systems of inequalities and equations given, we will handle each part separately.

1. Solving the inequality:

   We start with the inequality \( 2x > -8 \).

   Divide both sides by 2:

   \[ x > -4 \]

   So, the solution set for this inequality is \( {x | x > -4} \).

2. Solving the equation:

   Next, we solve the equation \( -5x + 7 = 12 \).

   Subtract 7 from both sides:

   \[ -5x = 12 - 7 \]

   \[ -5x = 5 \]

   Divide both sides by -5 (remember to flip the inequality):

   \[ x = -1 \]

   So the solution to this equation is \( {-1} \).

Now, combining both results:

• The inequality gives us \( x > -4 \).
• The equation gives us \( x = -1 \).

In terms of the responses provided, the inequality \( x > -4 \) is satisfied by \( x = -1 \), as \(-1\) is greater than \(-4\).

Thus, the solution sets can be written as:

• Inequality: \( {x | x > -4} \)
• Equation: \( {-1} \)

From the responses given, the correct choice is:

{x | x > −4}.