Question

3/7x -1/7 <_ 1 6/7

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we need to find the value of x that satisfies the inequality.

First, let's simplify the inequality:
3/7x - 1/7 ≤ 1 6/7

To make it easier to compare, let's convert 1 6/7 to an improper fraction:
1 6/7 = (7/7 * 1) + 6/7 = 7/7 + 6/7 = 13/7

Now our inequality becomes:
3/7x - 1/7 ≤ 13/7

Next, let's clear the fractions by multiplying through by 7:
7(3/7x - 1/7) ≤ 7(13/7)

This simplifies to:
3x - 1 ≤ 13

Now, let's isolate the variable x by adding 1 to both sides of the inequality:
3x - 1 + 1 ≤ 13 + 1
3x ≤ 14

Finally, divide both sides of the inequality by 3:
(3x)/3 ≤ 14/3
x ≤ 14/3

Therefore, the solution to the inequality is x ≤ 14/3.

Answer 2

on a number lune

Answer 3

[AI-generated answer — Bot GPT 3.5]

On a number line, the solution x ≤ 14/3 would be represented by shading all the numbers to the left of or on the point 14/3. The point 14/3 would be included in the shading since the inequality is a less than or equal to sign.

Answer 4

1/5x -3/5 <_ 2/5

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the inequality 1/5x - 3/5 ≤ 2/5, we will follow similar steps as before.

First, let's simplify the inequality:
1/5x - 3/5 ≤ 2/5

Next, let's clear the fractions by multiplying through by 5:
5(1/5x) - 5(3/5) ≤ 5(2/5)

This simplifies to:
x - 3 ≤ 2

Now, let's isolate the variable x by adding 3 to both sides of the inequality:
x - 3 + 3 ≤ 2 + 3
x ≤ 5

Therefore, the solution to the inequality is x ≤ 5.

On a number line, this would be represented by shading all the numbers to the left of or on the point 5. The point 5 would be included in the shading since the inequality is a less than or equal to sign.

Answer 6

9.5 - 1.25 < 32 on a number line

Answer 7

[AI-generated answer — Bot GPT 3.5]

To represent 9.5 - 1.25 < 32 on a number line, let's first evaluate the expression:

9.5 - 1.25 = 8.25

So, we have 8.25 < 32.

On a number line, we can represent this inequality by placing a closed circle or dot on 8.25 and shading all the numbers to the left of it until 32.

Here's an illustration:

-------------------●----------------------32

The shaded portion would represent all the numbers less than 32, including 8.25.

Answer 8

9.5x - 1.25 < 32 on a number line

Answer 9

[AI-generated answer — Bot GPT 3.5]

To represent the inequality 9.5x - 1.25 < 32 on a number line, we need to solve for x and then plot the solutions on the number line.

Let's solve the inequality:
9.5x - 1.25 < 32

Add 1.25 to both sides of the inequality:
9.5x - 1.25 + 1.25 < 32 + 1.25
9.5x < 33.25

Divide both sides of the inequality by 9.5:
(9.5x)/9.5 < 33.25/9.5
x < 3.5

Therefore, the solution to the inequality is x < 3.5.

On a number line, we represent this inequality by placing an open circle or dot on 3.5 and shading all the numbers to the left of it. Since the inequality is strict (less than), we do not include the point 3.5 in the shading.

Here's an illustration:

----------------------o-----------------3.5