Question

Consider the inequality 3( - 1 - x) ≤ -2x - 3x.

The solution set of the inequality is:

(1 point)
Responses

A) {x|x≥32}
{x|xis greater than or equal to 3 halves}

B) {x|x≤32}
{x|xis less than or equal to 3 halves}

C) {x|x≥23}
{x|xis greater than or equal to 2 thirds}

D){x|x≤23}
Answer
Graph the previous solution set on a number line.(1 point)
Responses
Answer
Solve the inequality: -2(2x - 4) ≤ 4(2 - x).(1 point)
Responses
Answer
Which values are in the solution set of the inequality −23x + 13 ≥ −1 ?
Answer
Which values are in the solution set of the inequality −23x + 13 ≥ −1 ?

19
20
21
22
or 23
Answered by GPT 3.5
To solve the inequality, we need to simplify both sides and then solve for x.

Starting with the left side of the inequality, we distribute the 3 to both terms inside the parentheses:
3(-1 - x) = -3 - 3x.

Now let's simplify the right side of the inequality:
-2x - 3x = -5x.

Plugging these simplified expressions back into the original inequality, we have:
-3 - 3x ≤ -5x.

Next, let's get all the x terms on one side of the inequality by adding 5x to both sides:
-3 + 2x ≤ 0.

Now, let's isolate the x term by adding 3 to both sides:
2x ≤ 3.

Finally, divide both sides by 2 to solve for x:
x ≤ 3/2.

So the solution set of the inequality is {x | x ≤ 3/2}.

Therefore, the correct answer is:
B) {x | x ≤ 3/2}.
Answered by GPT 3.5
I'm sorry, but as a text-based AI, I am unable to directly generate graphical representations. However, I can describe how to graph the solution set on a number line.

To graph the solution set {x | x ≤ 3/2} on a number line, you would first draw a horizontal line with a labeled point at 3/2. Then, shade the region to the left of and including the point 3/2, to represent all the values of x that satisfy the inequality x ≤ 3/2.

I apologize for any inconvenience caused.
Answered by GPT 3.5
Let's simplify the inequality step by step.

Starting with the left side of the inequality, we distribute the -2 to both terms inside the parentheses:
-2(2x - 4) = -4x + 8.

Now let's simplify the right side of the inequality:
4(2 - x) = 8 - 4x.

Plugging these simplified expressions back into the original inequality, we have:
-4x + 8 ≤ 8 - 4x.

Next, let's get all the x terms on one side of the inequality by adding 4x to both sides:
8 ≤ 8.

No matter the value of x, the inequality 8 ≤ 8 is always true. Therefore, the solution set for this inequality is all real numbers or (-∞, ∞).

Thus, the correct answer is:
{x | x is a real number} or (-∞, ∞).
Answered by GPT 3.5
To solve the inequality, we need to isolate the variable x.

Starting with the inequality:
-23x + 13 ≥ -1.

First, let's subtract 13 from both sides:
-23x ≥ -14.

Next, divide both sides by -23. Remember that when dividing by a negative number, the direction of the inequality sign should be flipped:
x ≤ -14/-23.

Simplifying the expression on the right side:
x ≤ 14/23.

So, the values in the solution set of the inequality are all values of x that are less than or equal to 14/23.

Therefore, the correct answer is:
{x | x ≤ 14/23}.
Answered by GPT 3.5
To determine which values are in the solution set of the inequality −23x + 13 ≥ −1, we need to solve the inequality for x.

Starting with the inequality:
-23x + 13 ≥ -1

We can isolate the variable x by subtracting 13 from both sides:
-23x ≥ -1 - 13
-23x ≥ -14

Next, divide both sides by -23. Remember that when dividing by a negative number, the direction of the inequality sign should be flipped:
x ≤ -14/ -23

Simplifying the expression:
x ≤ 14/ 23

So, the values in the solution set of the inequality are all values of x that are less than or equal to 14/23.

Among the given options, the value that satisfies x ≤ 14/23 is 19.

Therefore, the correct answer is:
19