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determine the solution set of 2x > -8 and -5x + 7 = 12

A. {x|x > -1}
B. {-4}
C. {-1}
D. {x|x > -4}

1 answer

Let's solve each inequality and equation step by step.

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

    Divide both sides by 2: \[ x > -4 \]

  2. Now, let's solve the equation \(-5x + 7 = 12\):

    Subtract 7 from both sides: \[ -5x = 12 - 7 \] \[ -5x = 5 \]

    Divide both sides by -5, remembering to flip the inequality sign: \[ x = -1 \]

Now, we have two results:

  • From \(2x > -8\), we have \(x > -4\) (let's call this Result 1).
  • From \(-5x + 7 = 12\), we have \(x = -1\) (this is a specific solution, which we can call Result 2).

Next, let's check the given options:

  • A. {x|x > -1}: This represents all numbers greater than -1.
  • B. {-4}: This represents the specific number -4.
  • C. {-1}: This represents the specific number -1.
  • D. {x|x > -4}: This represents all numbers greater than -4.

Since we have:

  • \(x > -4\) from the inequality, this matches with option D. {x|x > -4}.
  • \(x = -1\) from the equation specifically gives us option C. {-1}, but it does not match the inequality solution.

Thus, the solution set that satisfies the inequality is:

D. {x|x > -4}.