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

Question

Responses:

{x|x>−1}

{−4}

{x|x>−4}

{−1}

Answer 1

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: $x|x>-4$

Answer 2

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

The solution set is null.

{−1,3}

{3}

{−1}

Answer 3

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: $-1,3$