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

{−4}
left brace negative 4 right brace

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

{−1}
left brace negative 1 right brace

{x|x>−4}

Answer 1

To solve the problem, we need to tackle each inequality and equation separately.

1. Solve the inequality \(2x > -8\): \[ 2x > -8 \] Divide both sides by 2: \[ x > -4 \] So, the solution set for this inequality is \( { x , | , x > -4 } \).

2. Solve the equation \(-5x + 7 = 12\): \[ -5x + 7 = 12 \] Subtract 7 from both sides: \[ -5x = 5 \] Divide both sides by -5: \[ x = -1 \]

Now, we have the solution sets:

• From the inequality: \( { x , | , x > -4 } \)
• From the equation: \( {-1} \)

To find the combined solution set that satisfies both conditions, we note that \(x = -1\) does satisfy \(x > -4\).

Thus, the solution set includes the value obtained from the equation, which is \({-1}\).

So, the final answer is: \[ {-1} \]