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

Question

{-1}
{-4}
{ x| x > -1}
{ x| x > -4}

Answer 1

To solve the inequalities and the equation given in the problem, we'll analyze each one step by step.

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

   To isolate \(x\), divide both sides of the inequality by 2: \[ x > -4 \]

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

   First, subtract 7 from both sides: \[ -5x = 12 - 7 \] \[ -5x = 5 \]

   Next, divide both sides by -5 (remember to reverse the inequality sign when dividing by a negative number): \[ x = -1 \]

3. Determining the solution set:

   The solution to the inequality \(x > -4\) gives us all numbers greater than -4, while the solution to the equation gives us a specific value \(x = -1\).

   The solution set will depend on where these solutions overlap or what they suggest:

   • The inequality \(x > -4\) indicates that any number greater than -4 is valid.
   • The specific solution from the equation is \(x = -1\), which is valid since -1 is indeed greater than -4.

Given these analyses, we can select the correct representation of the solution sets:

• \( { x | x > -4 } \) includes all numbers greater than -4, whereas \( { x | x > -1 } \) would only include numbers greater than -1, which does not incorporate the entire range given by the inequality.

Thus, the solution set of the inequality and the equation is expressed as: \[ { x | x > -4 } \]

So the correct answer is \({ x | x > -4 }\).

Answer 2

Determine the solution set of -3x + 7 = 10 or 3x - 9 = 0.
{-1}
{3}
{-1,3}
The solution set is null.

Answer 3

Let's solve the two equations provided in the problem one by one.

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

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

Now we have found two solutions:

• From the first equation: \(x = -1\)
• From the second equation: \(x = 3\)

Since the solution is given in terms of "or," we combine both solutions:

The complete solution set is: \[ {-1, 3} \]

Thus, the correct answer is: \({-1, 3}\)