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

Responses

{−1}
left brace negative 1 right brace

{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

{−4}

1 answer

Let's solve the inequalities and equations step by step.

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

    Divide both sides by 2: \[ x > -4 \] This gives us the solution set \( {x | x > -4} \).

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

    First, subtract 7 from both sides: \[ -5x = 12 - 7 \] \[ -5x = 5 \] Now, divide both sides by -5 (remember to reverse the inequality): \[ x = -1 \]

Now we have two results:

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

Since \(-1\) is greater than \(-4\), it is included in the solution of the inequality.

Therefore, the answer to the problem is: \[ {x | x > -4} \text{, which includes } {-1}. \]

So the best match from the provided responses is: \( {x | x > -4} \)