Question 1

Solve the inequality $$6 - (x + 5) \geq 6 - 6x$$ and express the solution set in interval notation.

Accepted Answer

$$[0, \infty)$$

Question 2

Which of the following is the correct first step to solve the inequality $$6 - (x + 5) \geq 6 - 6x$$?

Accepted Answer

Expand $$6 - (x + 5) to$$ $$6 - x - 5$$

Question 3

After simplifying $$6 - (x + 5) \geq 6 - 6x$$, what is the resulting inequality?

Accepted Answer

$$1 - x \geq 6 - 6x$$

Question 4

Solve for $$x in $$the inequality $$1 - x \geq 6 - 6x.$$

Accepted Answer

$$x \geq 0$$

Question 5

Which of the following graphs correctly represents the solution set $$[0, \infty) on a $$number line?

Accepted Answer

A filled circle at $$0$$ and shading to the right

Question 6

If the solution set to an inequality is $$[0, \infty)$$, which of the following statements is true?

Accepted Answer

All real numbers greater than or equal to $$0$$ are solutions.

Question 7

Which interval notation represents all real numbers $$x$$ such that $$x \geq 0$$?

Accepted Answer

$$[0, \infty)$$

Question 8

Suppose you are solving $$6 - (x + 5) \geq 6 - 6x$$ for a chemical concentration $$x in a $$reaction. If $$x$$ represents the concentration in mol/L, what is the minimum concentration allowed by the solution set?

Accepted Answer

$$0$$ mol/L

Question 9

If the solution set to an inequality is $$\emptyset$$, what does this mean about the solutions?

Accepted Answer

There are no solutions.

Question 10

Which of the following is a correct way to check if $$x = 2 is a $$solution to $$6 - (x + 5) \geq 6 - 6x$$?

Accepted Answer

Substitute $$x = 2$$ into both sides and check if the left side is greater than or equal to the right side.

Question 11

Which of the following intervals does NOT include $$0$$?

Accepted Answer

$$(0, \infty)$$

Question 12

If the solution set to an inequality is $$[0, \infty)$$, which of the following values is NOT a solution?

Accepted Answer

$$-1$$

Question 13

Which of the following best describes the process of expressing a solution set in interval notation?

Accepted Answer

Use brackets and parentheses to indicate the set of all solutions within a range.

Question 14

If you graph the solution set $$[0, \infty) on a $$number line, which of the following is true?

Accepted Answer

The graph starts at $$0$$ with a filled circle and extends to the right.

Question 15

Which of the following is the correct interval notation for the solution set of $$x \geq 0$$?

Accepted Answer

$$[0, \infty)$$

Solving Linear Inequalities and Expressing Solution Sets in Interval Notation

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