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

Answer 1

To solve the given inequalities and equations, we can break them down step-by-step.

1. Solve the inequality: $2x>-8$

   To isolate $x$, divide both sides by 2:

   $$x>-4$$

2. Solve the equation: $-5x+7=12$

   First, subtract 7 from both sides:

   $$-5x=12-7$$

   $$-5x=5$$

   Next, divide both sides by -5 (remember that dividing by a negative number flips the inequality):

   $$x=-1$$

3. Combine the results

   We have:

   • From the inequality $2x>-8$, we found $x>-4$.
   • From the equation $-5x+7=12$, we found $x=-1$.

Now, let's determine if $x=-1$ satisfies the inequality $x>-4$:

Since $-1>-4$ is true, it is part of the solution set.

Thus, the solution set consists of the point from the equation and the inequality limits:

The solution set is:

$$x=-1\text{ for }2x>-8$$ or more generally, expressed with respect to the inequality:

$$x\in (-4,\mathrm{\infty })\text{ includes }x=-1$$

The complete solution set includes $x=-1$ as it satisfies both the inequality and the equation.