Respuesta :
Answer:
Part A:
Starting with −7(x − 4) < 84:
Distribute the -7 to get -7x + 28 < 84.
Subtract 28 from both sides to get -7x < 56.
Divide both sides by -7, remembering that dividing by a negative number flips the inequality sign, to get x > -8.
Therefore, the solution to the inequality is x > -8.
Part B:
To graph the solution to the inequality on a number line, we would start by drawing a number line and marking a point at -8. Since the solution is x > -8, we would draw an open circle at -8 to indicate that -8 is not included in the solution. Then, we would draw an arrow pointing to the right to indicate that all values greater than -8 are included in the solution.
Part C:
To find two values that would make the inequality true, we can choose any two values greater than -8 and substitute them into the inequality to see if they satisfy it. For example, if we choose x = 0, we get:
-7(0 - 4) < 84
-7(-4) < 84
28 < 84
Since 28 is less than 84, this inequality is true when x = 0. Similarly, if we choose x = 10, we get:
-7(10 - 4) < 84
-7(6) < 84
-42 < 84
Since -42 is less than 84, this inequality is also true when x = 10. We know these values are solutions to the inequality because they make the inequality true when substituted into it.
Hope that helps!
