Question

-2x+5+x<_3x+13 as a number line

Answer 1

[AI-generated answer — Bot GPT 3.5]

To represent the inequality -2x + 5 + x ≤ 3x + 13 on a number line, we can start by simplifying the expression.

Combining like terms, we have: -x + 5 ≤ 3x + 13

Next, we can get rid of the variable x on the left side by adding x to both sides: -x + x + 5 ≤ 3x + x + 13

This simplifies to: 5 ≤ 4x + 13

Now, subtracting 13 from both sides: 5 - 13 ≤ 4x + 13 - 13

This gives us: -8 ≤ 4x

Lastly, dividing both sides by 4 to solve for x: -8/4 ≤ 4x/4

Simplifying further: -2 ≤ x

Therefore, the solution to the inequality -2x + 5 + x ≤ 3x + 13 is x ∈ (-∞, -2]. This can be represented on a number line as follows:

---o---o---o---o---o---o---o---o---o---o---o---o---o---o---o---o---o---o---

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Answer 2

-2 ≤ x as a number line

Answer 3

[AI-generated answer — Bot GPT 3.5]

To represent the inequality -2 ≤ x on a number line, we can simply mark a closed circle at -2 and shade everything to the right of it.

---o---------------------------------------------------

-4 -3 -2 -1 0 1 2 3 4 5 6

Answer 4

Oh no! Max spilled his orange juice on his algebra work as he was finishing the problem below. What is a possible first step covered by the orange juice?

3t+2<-7 or `-4t+5<1`

Answer 5

[AI-generated answer — Bot GPT 3.5]

Since Max spilled orange juice on the problem, it is difficult to determine the exact equation he was working on. However, we can see that there are two separate inequalities on either side of "or" operator (`|`).

One possible interpretation of the first step that could be covered by the orange juice is:

3t + 2 < -7

Please note that without further clarification on which specific equation or side was affected by the orange juice spill, it's difficult to provide an accurate response.

Answer 6

Oh no! Max spilled his orange juice on his algebra work as he was finishing the problem below. What is a possible first step covered by the orange juice?

3t+2<-7 or `-4t+5<1`
−4t + 5 −5 < 1 − 5
−4t + 5 +10 < 1 − 5
−4t + 5 · 5 < 1 · −5
−4t + 5 +1 < 1 − 5

Answer 7

[AI-generated answer — Bot GPT 3.5]

Based on the steps covered by the orange juice spill, it appears that the affected equation is `-4t + 5 < 1`. Here is a possible first step before it got covered:

Subtract 5 from both sides:
−4t + 5 - 5 < 1 - 5

After simplification, it becomes:
−4t < -4

Answer 8

-7\le2x+1<11 as a number line

Answer 9

[AI-generated answer — Bot GPT 3.5]

To represent the inequality -7 ≤ 2x + 1 < 11 on a number line, we need to break it down into two separate inequalities.

First, let's solve for the left side:

-7 ≤ 2x + 1

Subtract 1 from both sides:

-8 ≤ 2x

Divide both sides by 2:

-4 ≤ x

So, the left inequality is: -4 ≤ x

Next, let's solve for the right side:

2x + 1 < 11

Subtract 1 from both sides:

2x < 10

Divide both sides by 2:

x < 5

So, the right inequality is: x < 5

Now, we can represent these inequalities on a number line:

-∞─────o─────o─────o─────o─────o─────o─────o─────o─────o─────o─────o─────o─────o─────o─────o─────o─────o─────o─────∞
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

On the number line, we represent -4 ≤ x by shading or marking a closed circle at -4 and shading everything to the right. Similarly, we represent x < 5 by marking an open circle at 5 and shading everything to the left.

The combined representation looks like:

-∞─────o─────o─────o─────o─────o─────o─────o─────o────o─────o─────o─────o─────o─────o─────o─────o─────o─────o─────∞
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

Answer 10

12x − 3 ≥ 15x or −0..2x + 10 < 5

Which choice best describes the solution set?
1 ≤ x < −25
−1 ≤ x < 25
x ≥ 1 or x < −25
x ≤ −1or x > 25

Answer 11

[AI-generated answer — Bot GPT 3.5]

The solution set for the given inequalities `-7≤2x+1<11` is described by the choice: x ≥ 1 or x < -25.

Answer 12

Tom have 25 days to pay is speeding ticket. This is represented by the inequality x`\ge`25

Answer 13

[AI-generated answer — Bot GPT 3.5]

I understand that Tom has 25 days to pay his speeding ticket, which can be represented by the inequality x ≥ 25. This means that the number of days (x) must be greater than or equal to 25 in order for Tom to pay his ticket on time.

Answer 14

Write an inequality to collect points. Maximize your score.

To earn the extra credit, your score must be at least 7.

You have collected 0 blue points and 0 red points.

Your score is 0.
blue = positive number

red = negative number

1 blue + 1 red = 0

Answer 15

[AI-generated answer — Bot GPT 3.5]

To maximize your score and earn extra credit, we can set up the following inequality:

1 blue + 1 red ≥ 7

This inequality ensures that your score, which is the sum of the blue points and the red points, must be greater than or equal to 7 to earn the extra credit.