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

Responses:

{x|x>−1}

{−4}

{x|x>−4}

{−1}

3 answers

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

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

  2. Solving the equation \(-5x + 7 = 12\): \[ -5x + 7 = 12 \] Subtract 7 from both sides: \[ -5x = 5 \] Divide both sides by -5 (and remember to reverse the inequality): \[ x = -1 \]

Now we combine our solutions:

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

Now, let's compare this to the provided options:

  1. \({x | x > -1}\)
  2. \({-4}\)
  3. \({x | x > -4}\)
  4. \({-1}\)

The correct solution set based on the inequality \(2x > -8\) is \({x | x > -4}\).

Final Answer: \({x | x > -4}\)

Determine the solution set of −3x+7=10 or 3x−9=0 .(1 point)
Responses

The solution set is null.

{−1,3}

{3}

{−1}

Let's solve the equations step by step.

  1. Solving the equation \(-3x + 7 = 10\): \[ -3x + 7 = 10 \] Subtract 7 from both sides: \[ -3x = 3 \] Divide both sides by -3: \[ x = -1 \]

  2. Solving the equation \(3x - 9 = 0\): \[ 3x - 9 = 0 \] Add 9 to both sides: \[ 3x = 9 \] Divide both sides by 3: \[ x = 3 \]

Now we combine the solutions from both equations:

  • From \(-3x + 7 = 10\), we have \(x = -1\).
  • From \(3x - 9 = 0\), we have \(x = 3\).

So, the solution set is \(-1\) and \(3\), which can be expressed as \({-1, 3}\).

Now, let's compare this to the provided options:

  1. The solution set is null.
  2. \({-1, 3}\)
  3. \({3}\)
  4. \({-1}\)

Final Answer: \({-1, 3}\)