Question

Solve 8x+4≥52 .(1 point)

x≥6

x≥2.5

x≥7


x≥11

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality 8x + 4 ≥ 52, we need to isolate x.

First, subtract 4 from both sides:

8x + 4 - 4 ≥ 52 - 4
8x ≥ 48

Next, divide both sides by 8:

8x/8 ≥ 48/8
x ≥ 6

So, the solution to the inequality is x ≥ 6.

Answer 2

Solve 1/4x − 3/4 > 5 1/4.(1 point)

Responses

x>18

x>21 3/4

x>1 1/2


x>24

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve the inequality (1/4)x - 3/4 > 5 1/4, we need to isolate x.

First, let's simplify the right side of the inequality:

5 1/4 = 5 + 1/4 = 20/4 + 1/4 = 21/4

So, the inequality becomes:

(1/4)x - 3/4 > 21/4

Next, add 3/4 to both sides:

(1/4)x - 3/4 + 3/4 > 21/4 + 3/4
(1/4)x > 24/4

Simplifying further:

(1/4)x > 6

To isolate x, multiply both sides by 4:

(1/4)x * 4 > 6 * 4
x > 24

So, the solution to the inequality is x > 24.

Answer 4

Solve the inequality 6x+9>57 .

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the inequality 6x + 9 > 57, we need to isolate x.

First, subtract 9 from both sides:

6x + 9 - 9 > 57 - 9
6x > 48

Next, divide both sides by 6:

6x/6 > 48/6
x > 8

So, the solution to the inequality is x > 8.

Answer 6

show this answer on a number line

Answer 7

[AI-generated answer — Bot GPT 3.5]

To represent the solution x > 8 on a number line, we will draw an open circle at 8 and shade the region to the right of 8. This indicates that any value of x that is greater than 8 satisfies the inequality.

Here's a visual representation:

```
------>
8
```

The arrow indicates that the solution extends infinitely to the right.

Answer 8

1/5x − 3/5 ≤ 2/5

2/5x − 4/5 ≥ 1 1/5

3/5x + 2/5 ≥ 3 2/5


3/7x + 1/7 ≤ 1 6/7

Answer 9

[AI-generated answer — Bot GPT 3.5]

To represent the solutions on a number line, we will first solve each inequality and then plot the solutions.

1. (1/5)x - 3/5 ≤ 2/5:
Add 3/5 to both sides:
(1/5)x ≤ 2/5 + 3/5
(1/5)x ≤ 5/5
(1/5)x ≤ 1
Multiply both sides by 5 (note that when we multiply or divide by a negative number, the direction of the inequality symbol reverses):
x ≤ 5
This solution can be represented by shading the region to the left of or including 5 on the number line, and placing a closed circle at 5.

2. (2/5)x - 4/5 ≥ 1 1/5:
Simplify 1 1/5 to 6/5
Add 4/5 to both sides:
(2/5)x ≥ 6/5 + 4/5
(2/5)x ≥ 10/5
(2/5)x ≥ 2
Multiply both sides by 5/2 (note that we reverse the inequality symbol because we're dividing by a negative number):
x ≥ 5/2
This solution can be represented by shading the region to the right of or including 5/2 on the number line, and placing a closed circle at 5/2.

3. (3/5)x + 2/5 ≥ 3 2/5:
Simplify 3 2/5 to 17/5
Subtract 2/5 from both sides:
(3/5)x ≥ 17/5 - 2/5
(3/5)x ≥ 15/5
(3/5)x ≥ 3
Multiply both sides by 5/3 (note that we reverse the inequality symbol because we're dividing by a negative number):
x ≥ 5/3
This solution can be represented by shading the region to the right of or including 5/3 on the number line, and placing a closed circle at 5/3.

4. (3/7)x + 1/7 ≤ 1 6/7:
Simplify 1 6/7 to 13/7
Subtract 1/7 from both sides:
(3/7)x ≤ 13/7 - 1/7
(3/7)x ≤ 12/7
Multiply both sides by 7/3:
x ≤ 12/3
x ≤ 4
This solution can be represented by shading the region to the left of or including 4 on the number line, and placing a closed circle at 4.

Here is the representation on the number line:

```
-∞---|----|----|----|---4---5---∞
4 5
```

The shaded regions and the closed circles indicate the solutions for each inequality.

Answer 10

put them each on a number line

Answer 11

[AI-generated answer — Bot GPT 3.5]

Sure! Here are the number lines representing the solutions for each inequality:

1. (1/5)x - 3/5 ≤ 2/5:
```
-∞---|----|----|----|----|----1---∞
1
```
2. (2/5)x - 4/5 ≥ 1 1/5:
```
-∞---|----|----|---|----1 1/2---∞
1 1/2
```
3. (3/5)x + 2/5 ≥ 3 2/5:
```
-∞---|----|---5/3---|----∞
5/3
```
4. (3/7)x + 1/7 ≤ 1 6/7:
```
-∞---|---4/7---|---∞
4/7
```

Each number line shows the solution intervals for each inequality. The shaded regions and closed circles indicate the values that satisfy each inequality.