1)
Working with inequalities, when you draw them in a number line or a coordinate system. The Open circle, or "blank dot" indicates that the number itself is not included in the definition, while the closed circle or "blak dot" indicates the value is included.
For example:
The inequality marked in the number line can be expressed symbolically as:
[tex]x<2[/tex]
So the first statement is True.
2)
When an inequality includes a variable (letter) this one can be writen in terms of said variable following almost the same rules as when you calculate the value of a variable in an equation.
The greatest exception is that when you divide by a negative number, the direction of the inequality changes.
So for the given inequality:
[tex]-10w>100[/tex]
To determine one possible value of w you have to divide both sides of the expression by "-10" and when you do so, the direction of the inequality gets inverted from > to <
[tex]\begin{gathered} -10w>100 \\ w<\frac{100}{-10} \\ w<-10 \end{gathered}[/tex]
So this statement is False.
3)
This statement is True, when the variable is "alone" the coefficient is 1. Since multiplying a number by one results in said number it is redundant to write it, but altough "invisible" one is the coefficient of any variable that is "alone" in any given expression.
4)
"At most" indicates that it is the maximum value possible for the determined inequality. So the inequality can be equal or less than the determined value.
For example, "The cell phone repair will cost at most $100" → You know that you will pay no more than $100 dollars for the repair, it can be less but not more.
Let "x" symbolize the repair cost, you can express this as:
[tex]x\leq100[/tex]
So this statement is True
5)
"Minimum" indicates that is the lowest value of the inequality, it is the startpoint, from the determined value onwards.
