Try to isolate a variable in each inequality. Then, try to interpret the inequality in terms of the relationship between two variables.
b
Practice makes perfect
We want to order a, b, c, and d from least to greatest. Let's look at the given inequalities!
lcc-3 ≥ d & (I) b+4 < a+1 & (II) a-2 ≤ d-7 & (III)
We will start by simplifying the inequalities so that one of the variables is isolated on one side of the inequality.
lcc-3 ≥ d & (I) b+4 < a+1 & (II) a-2 ≤ d-7 & (III)
First inequality tells us that even after subtracting 3 from c, this expression is still greater than or equal to d. This means that c itself must be greater than d.
Let's analyze all inequalities in a similar way!
Inequality
Description
Conclusion
c-3 ≥ d
After subtracting 3 from c, the value is still greater than or equal to d.
c> d
b+3 < a
After adding 3 to b, the value is still less than a.
b< a
a+5 ≤ d
After adding 5 to a, the value is still less than or equal to d.
a< d
Notice that the second inequality tells us that b is less than a, and the third inequality tells us that at the same time a is less than d. With this information we can order these three values.
b< a & a< d
⇓
b< a < d
Now we can use the information given by the first inequality. It states that c is greater than d. Notice that we already know that d is greater than both a and b. This means that if c is greater than d, then c is the greatest of all given values.
b< a < d & c> d
⇓
b< a < d < c
