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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