Question

8x + 4 _> 52

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Subtracting 4 from both sides of the inequality, we have:
8x + 4 - 4 ≥ 52 - 4
8x ≥ 48

Now, divide both sides of the inequality by 8:
8x/8 ≥ 48/8
x ≥ 6

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

Answer 2

1/4x - 3/4 > 5 1/4

Answer 3

[AI-generated answer — Bot GPT 3.5]

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

First, let's convert the mixed number 5 1/4 to an improper fraction.

5 1/4 = 21/4

Now, rewrite the inequality:

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

To eliminate the denominators, multiply the entire inequality by 4:

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

Simplifying:

x - 3 > 21

Next, add 3 to both sides of the inequality:

x - 3 + 3 > 21 + 3

x > 24

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

Answer 4

6x +9 > 57 on a number line

Answer 5

[AI-generated answer — Bot GPT 3.5]

To represent the inequality 6x + 9 > 57 on a number line, we need to find the value of x that makes the inequality true.

First, subtract 9 from both sides of the inequality:
6x + 9 - 9 > 57 - 9
6x > 48

Next, divide both sides of the inequality by 6:
(6x)/6 > 48/6
x > 8

Therefore, any value of x greater than 8 will satisfy the inequality. On a number line, we can represent this solution by shading the region to the right of 8, indicating that all values greater than 8 are solutions.

Answer 6

so the point would goign tward to right? be one 8?

Answer 7

[AI-generated answer — Bot GPT 3.5]

Yes, that's correct! The point on the number line would go towards the right, to the side of the number 8. It indicates that any value of x greater than 8 would satisfy the given inequality, while values less than or equal to 8 would not.

Answer 8

2/5x -4/5 _> 1 1/5

Answer 9

[AI-generated answer — Bot GPT 3.5]

To solve the inequality 2/5x - 4/5 ≥ 1 1/5, we need to isolate the variable x.

First, let's rewrite 1 1/5 as an improper fraction:

1 1/5 = 6/5

Now, we can rewrite the inequality:

2/5x - 4/5 ≥ 6/5

To eliminate the denominators, we can multiply both sides of the inequality by 5:

5 * (2/5x - 4/5) ≥ 5 * (6/5)

Simplifying:

2x - 4 ≥ 6

Next, add 4 to both sides of the inequality:

2x - 4 + 4 ≥ 6 + 4

2x ≥ 10

Finally, divide both sides of the inequality by 2:

(2x)/2 ≥ 10/2

x ≥ 5

Therefore, the solution to the inequality is x ≥ 5. On a number line, this would be represented by shading the region to the right of 5, since any value of x equal to or greater than 5 satisfies the inequality.