Question

1. according to the lesson 13 summary, why do we use inequalities?

to make equations more complicated
to represent one solution
to describe a range of numbers

1. the solutions to the inequality -2x≥10 are different from the solutions to -2x>10.

true
false

Explanation:

Question 2

Inequalities are not used to complicate equations (first option is wrong). They also don't represent one solution (equations do that for specific cases, inequalities represent a range). The correct reason is to describe a range of numbers.

Step1: Solve \(-2x \geq 10\)

Divide both sides by \(-2\) (remember to reverse the inequality sign): \(x \leq -5\).

Step2: Solve \(-2x > 10\)

Divide both sides by \(-2\) (reverse the inequality sign): \(x < -5\).

Step3: Compare solutions

The solution to \(-2x \geq 10\) includes \(x = -5\), while the solution to \(-2x > 10\) does not. So the solutions are different.

Answer:

to describe a range of numbers

Question 3