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1. Determine the solution set of 2x>−8

and −5x+7=12
(1 point)
Responses

{−1}
start set negative 1 end set

{x|x>−1}
start set x such that x is greater than negative 1 end set

{−4}
start set negative 4 end set

{x|x>−4}

1 answer

To determine the solution set for the inequalities and equations given, let's solve them step by step.

  1. For the inequality \(2x > -8\): \[ \frac{2x}{2} > \frac{-8}{2} \ x > -4 \] So the solution set for this inequality is \({x | x > -4}\).

  2. For the equation \(-5x + 7 = 12\): First, we'll isolate \(x\): \[ -5x + 7 = 12 \] Subtract 7 from both sides: \[ -5x = 12 - 7 \ -5x = 5 \] Now, divide by -5: \[ x = \frac{5}{-5} \ x = -1 \] The solution to this equation is \(-1\).

Now we have:

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

Since the problem asks for the overall solution set combining both, we observe:

  • The inequality \(x > -4\) is true for all numbers greater than -4.
  • The solution to the equation is \(-1\), and since \(-1\) is indeed greater than \(-4\), it fits within the range established by the inequality.

Thus, the solution includes both findings:

  • The inequality gives us a range of solutions, while the equation provides a specific solution.

Given the options provided, it seems the focus is to choose the correct response for the inequality result, which is:

{x | x > -4}.

So, the final conclusion can be summarized as:

  • Equation solution: {-1}
  • Inequality solution set: {x | x > -4}

If only one option must be selected as a general solution set based on the context you've provided, it could also focus on the inequality, following the logical relationship derived.

In a concise answer format, based on options:

  • The correct response that captures the inequality aspect is {x | x > -4}.