Question 1

Which of the following is the correct solution in interval notation for the inequality $$3x + 1 \geq 4x - 3(4x - 3)$$?

Accepted Answer

$$[\frac{8}{11}, \infty)$$

Question 2

When solving the inequality $$3x + 1 \geq 4x - 3(4x - 3)$$, what is the first step after distributing?

Accepted Answer

Combine like terms on the right side

Question 3

What is the result after distributing $$-3 to$$ $$(4x - 3) in $$the inequality $$3x + 1 \geq 4x - 3(4x - 3)$$?

Accepted Answer

$$-12x + 9$$

Question 4

After combining like terms, what does the inequality $$3x + 1 \geq 4x - 12x + 9$$ simplify to?

Accepted Answer

$$3x + 1 \geq -8x + 9$$

Question 5

Which property of inequalities requires you to reverse the inequality symbol?

Accepted Answer

Multiplying or dividing both sides by a negative number

Question 6

What is the solution to $$5x + 13 \u003c 36 in $$interval notation?

Accepted Answer

$$(-\infty, \frac{23}{5})$$

Question 7

If you multiply both sides of $$-2x \u003e 8 by$$ $$-1$$, what is the resulting inequality?

Accepted Answer

$$2x \u003c -8$$

Question 8

Which of the following is the correct interval notation for $$x \geq -3$$?

Accepted Answer

$$[-3, \infty)$$

Question 9

Solve the inequality $$2(x - 4) \leq 6$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, 7]$$

Question 10

A chemist needs the temperature $$T in a $$reaction to be at least $$23$$ degrees but less than $$80$$ degrees. Which interval represents the possible values for $$T$$?

Accepted Answer

$$[23, 80)$$

Question 11

Which of the following is the correct solution to $$-3x + 7 \u003e 1$$?

Accepted Answer

$$x \u003c 2$$

Question 12

If $$x$$ represents the number of hours a student studies and the requirement is $$x \u003e 4$$, which interval notation expresses this?

Accepted Answer

$$(4, \infty)$$

Question 13

Solve the inequality $$\frac{x + 5}{6} + \frac{x - 1}{9} \u003c 2$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, \frac{23}{5})$$

Question 14

A medical test is positive if $$x \leq 2.5. $$Which interval notation represents all possible positive results?

Accepted Answer

$$(-\infty, 2.5]$$

Question 15

Which of the following is a true statement about inequalities?

Accepted Answer

Adding or subtracting the same number from both sides does not change the inequality symbol.

Solving Linear Inequalities

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