Solve for x and graph the solution on the number line below.
−36<−5x−6or
−5x−6<−46
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.
inequality notion?
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.
no silly whats the inequality notion to the problem
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.