Question
Solve for x and graph the solution on the number line below.
−36<−5x−6or
−5x−6<−46
−36<−5x−6or
−5x−6<−46
Answers
Answer
inequality notion?
Answer
no silly whats the inequality notion to the problem
Answered by
GPT 3.5
To solve the inequality -36 < -5x - 6, we can start by adding 6 to both sides:
-36 + 6 < -5x - 6 + 6
-30 < -5x
Next, we divide both sides by -5, remembering that when dividing by a negative number, the inequality sign flips:
-30 / -5 > -5x / -5
6 > x
So, the solution to the first inequality is x > 6.
Now, let's solve the second inequality:
-5x - 6 < -46
We can start by adding 6 to both sides:
-5x - 6 + 6 < -46 + 6
-5x < -40
Next, we divide both sides by -5, remembering to flip the inequality sign:
-5x / -5 > -40 / -5
x > 8
So, the solution to the second inequality is x > 8.
To graph the solution on a number line, we mark the numbers 6 and 8 on the number line and shade the area to the right of those numbers, since x is greater than both 6 and 8.
Number line:
<-----|----|----|----|----|----|----|----|----|----|----|-->
-4 0 4 6 8 12 16 20 24 28 32 36
The shaded area is to the right of both 6 and 8.
-36 + 6 < -5x - 6 + 6
-30 < -5x
Next, we divide both sides by -5, remembering that when dividing by a negative number, the inequality sign flips:
-30 / -5 > -5x / -5
6 > x
So, the solution to the first inequality is x > 6.
Now, let's solve the second inequality:
-5x - 6 < -46
We can start by adding 6 to both sides:
-5x - 6 + 6 < -46 + 6
-5x < -40
Next, we divide both sides by -5, remembering to flip the inequality sign:
-5x / -5 > -40 / -5
x > 8
So, the solution to the second inequality is x > 8.
To graph the solution on a number line, we mark the numbers 6 and 8 on the number line and shade the area to the right of those numbers, since x is greater than both 6 and 8.
Number line:
<-----|----|----|----|----|----|----|----|----|----|----|-->
-4 0 4 6 8 12 16 20 24 28 32 36
The shaded area is to the right of both 6 and 8.
Answered by
GPT 3.5
The inequality notion refers to the symbols used to represent inequalities. The three common inequality symbols are:
1. < (less than): This symbol is used to indicate that one quantity is smaller than another. For example, 3 < 5 means that 3 is less than 5.
2. > (greater than): This symbol is used to indicate that one quantity is larger than another. For example, 7 > 4 means that 7 is greater than 4.
3. ≤ (less than or equal to): This symbol is used to indicate that one quantity is less than or equal to another. For example, 2 ≤ 2 means that 2 is less than or equal to 2.
4. ≥ (greater than or equal to): This symbol is used to indicate that one quantity is greater than or equal to another. For example, 6 ≥ 6 means that 6 is greater than or equal to 6.
These symbols are used to compare two quantities or express a range of values in mathematical inequalities.
1. < (less than): This symbol is used to indicate that one quantity is smaller than another. For example, 3 < 5 means that 3 is less than 5.
2. > (greater than): This symbol is used to indicate that one quantity is larger than another. For example, 7 > 4 means that 7 is greater than 4.
3. ≤ (less than or equal to): This symbol is used to indicate that one quantity is less than or equal to another. For example, 2 ≤ 2 means that 2 is less than or equal to 2.
4. ≥ (greater than or equal to): This symbol is used to indicate that one quantity is greater than or equal to another. For example, 6 ≥ 6 means that 6 is greater than or equal to 6.
These symbols are used to compare two quantities or express a range of values in mathematical inequalities.
Answered by
GPT 3.5
Apologies for the misunderstanding. The inequality notion for the given problem is the "or" symbol, represented as "∨".
The original inequality can be written as:
-36 < -5x - 6 ∨ -5x - 6 < -46
The symbol "∨" in this context is used to indicate that one of the two inequalities needs to be true for a solution to exist. In other words, either -36 < -5x - 6 or -5x - 6 < -46 must be satisfied.
The original inequality can be written as:
-36 < -5x - 6 ∨ -5x - 6 < -46
The symbol "∨" in this context is used to indicate that one of the two inequalities needs to be true for a solution to exist. In other words, either -36 < -5x - 6 or -5x - 6 < -46 must be satisfied.
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