Question 1

Solve the inequality $$3(x-1) - 5(x+1) \geq -2x - 2$$ and express the solution set in interval notation.

Accepted Answer

$$(-\infty, 2]$$

Question 2

Which of the following is the correct first step to solve $$3(x-1) - 5(x+1) \geq -2x - 2$$?

Accepted Answer

Expand both $$3(x-1)$$ and $$-5(x+1)$$

Question 3

After expanding and simplifying $$3(x-1) - 5(x+1) \geq -2x - 2$$, what is the resulting inequality?

Accepted Answer

$$-2x - 8 \geq -2x - 2$$

Question 4

What is the solution set to the inequality $$-2x - 8 \geq -2x - 2$$?

Accepted Answer

$$x \leq 2$$

Question 5

Which graph best represents the solution set $$(-\infty, 2] on a $$number line?

Accepted Answer

A ray starting at $$2$$ and extending to the left, with a closed circle at $$2$$

Question 6

If the inequality was $$3(x-1) - 5(x+1) \u003e -2x - 2$$, how would the solution set change?

Accepted Answer

$$(-\infty, 2)$$

Question 7

Which of the following is a value that satisfies $$3(x-1) - 5(x+1) \geq -2x - 2$$?

Accepted Answer

$$x = 2$$

Question 8

Suppose a chemical process is safe for $$x$$ values that satisfy $$3(x-1) - 5(x+1) \geq -2x - 2. $$For which range of $$x is $$the process safe?

Accepted Answer

$$x \leq 2$$

Question 9

If you mistakenly distribute $$-5 as$$ $$-5x - 1$$ instead of $$-5x - 5$$, what would be the incorrect simplified inequality?

Accepted Answer

$$-2x - 2 \geq -2x - 2$$

Question 10

Which step is necessary to isolate $$x in $$the inequality $$-2x - 8 \geq -2x - 2$$?

Accepted Answer

Add $$2x to $$both sides

Question 11

If the inequality was $$3(x-1) - 5(x+1) \leq -2x - 2$$, what would the solution set be?

Accepted Answer

Question 12

Which of the following is the correct interval notation for all $$x$$ less than or equal to $$2$$?

Accepted Answer

$$(-\infty, 2]$$

Question 13

If a medical dosage must satisfy $$3(x-1) - 5(x+1) \geq -2x - 2$$, what is the maximum safe dosage value for $$x$$?

Accepted Answer

$$x = 2$$

Question 14

Which of the following is NOT a valid step in solving $$3(x-1) - 5(x+1) \geq -2x - 2$$?

Accepted Answer

Multiplying both sides by $$-1$$ and reversing the inequality

Question 15

If you graph the solution set $$(-\infty, 2] on a $$number line, which point should be shaded?

Accepted Answer

The point at $$2$$

Solving Linear Inequalities and Expressing Solution Sets in Interval Notation

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