Question

make a random question about inequalities and answer it
Answer
with numbers like an equation
Answer
okay another one plz and use a number line
Answer
another one without number line but make it a little easy
Answer
plz another one
Answer
another
Answered by GPT 3.5
Question: What is the difference between strict inequality and non-strict inequality in mathematics?

Answer: In mathematics, inequalities are used to compare the relative sizes of two quantities. Strict inequality, denoted by "<" or ">", indicates that the quantities are not equal and one is strictly greater or smaller than the other. For example, if we have the inequality x > 5, it means that any value of x greater than 5 would satisfy the inequality, but x = 5 itself does not. Non-strict inequality, denoted by "≤" or "≥", includes the possibility of equality. For instance, if we have x ≥ 5, it means that any value of x greater than or equal to 5 would satisfy the inequality.
Answered by GPT 3.5
Question: Solve the inequality 2x + 3 > 7 and determine its solution set.

Answer: To solve the inequality 2x + 3 > 7, we need to find the range of values for x that make the inequality true.

First, we subtract 3 from both sides of the inequality to isolate the variable:

2x + 3 - 3 > 7 - 3
2x > 4

Next, we divide both sides by 2 to solve for x:

(2x)/2 > 4/2
x > 2

Therefore, the solution to the inequality 2x + 3 > 7 is x > 2. The solution set consists of all real numbers greater than 2.
Answered by GPT 3.5
Question: Solve the inequality 3x - 4 ≤ 10 and represent the solution on a number line.

Answer: To solve the inequality 3x - 4 ≤ 10 and represent it on a number line, we will follow these steps:

1. Add 4 to both sides of the inequality:
3x - 4 + 4 ≤ 10 + 4
3x ≤ 14

2. Divide both sides by 3 to isolate the variable:
(3x)/3 ≤ 14/3
x ≤ 4.67

Now, let's represent the solution x ≤ 4.67 on a number line:

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

Since the inequality states "x is less than or equal to 4.67," we will draw a solid dot at 4.67 on the number line and shade all the values to the left of it. This represents the solution set x ≤ 4.67.

◼--------------------|----|----|----|----|----|----|----|----|----|----|----
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Answered by GPT 3.5
Question: Solve the inequality 2(x - 1) > 8 and determine its solution set.

Answer: To solve the inequality 2(x - 1) > 8, we will simplify the expression and isolate the variable:

1. Distribute the 2 to the terms inside the parentheses:
2x - 2 > 8

2. Add 2 to both sides of the inequality:
2x - 2 + 2 > 8 + 2
2x > 10

3. Divide both sides by 2 to solve for x:
(2x)/2 > 10/2
x > 5

Therefore, the solution to the inequality 2(x - 1) > 8 is x > 5. The solution set consists of all real numbers greater than 5.
Answered by GPT 3.5
Question: Solve the inequality 3x + 7 ≥ -5 and determine its solution set.

Answer: To solve the inequality 3x + 7 ≥ -5, we will isolate the variable x:

1. Subtract 7 from both sides of the inequality:
3x + 7 - 7 ≥ -5 - 7
3x ≥ -12

2. Divide both sides by 3 to solve for x:
(3x)/3 ≥ -12/3
x ≥ -4

Therefore, the solution to the inequality 3x + 7 ≥ -5 is x ≥ -4. The solution set consists of all real numbers greater than or equal to -4.
Answered by GPT 3.5
Question: Solve the inequality 2x - 3 < 9 and determine its solution set.

Answer: To solve the inequality 2x - 3 < 9, we will isolate the variable x:

1. Add 3 to both sides of the inequality:
2x - 3 + 3 < 9 + 3
2x < 12

2. Divide both sides by 2 to solve for x:
(2x)/2 < 12/2
x < 6

Therefore, the solution to the inequality 2x - 3 < 9 is x < 6. The solution set consists of all real numbers less than 6.