Given:
The system of inequalities is:
To find:
The graph of the given system of inequalities.
Solution:
We have,
The related equations are:
Table of values for the given equations is:
0 1 -3
3 0 3
Plot (0,1) and (3,0) and connect them by a straight line to get the graph of .
Similarly, plot (0,-3) and (3,3) and connect them by a straight line to get the graph of .
The signs of both inequalities are ">". So, the boundary line is a dotted line and the shaded region or each inequality lie above the boundary line.
Therefore, the graph of the given system of inequalities is shown below.
Answer:
see explanation
Step-by-step explanation:
Inequalities of the type | x | ≤ a always have solutions of the form
- a ≤ x ≤ a
Given
| x - 1 | ≤ 1 then
- 1 ≤ x - 1 ≤ 1 ( add 1 to each of the 3 intervals )
0 ≤ x ≤ 2
Since we require an integer solution then x = 0, 1, 2
You add extra zeroes until all numbers have the same quantity. in this case, 2.303 has three numbers after the decimal, so the other three number need it too. 2.300, 2.330, and 2.030. now that you have all of them looking the same now, you can tell which is least and work from there: 2.030 is the least, then 2.300, 2.303 then 2.330 is the largest.
Answer:
Step-by-step explanation:
Let's rewrite the left side keeping in mind the next propierties:
Therefore:
Now, cancel logarithms by taking exp of both sides:
Multiply both sides by and using distributive propierty:
Substract from both sides and factoring:
Multiply both sides by -1:
Split into two equations:
Solving for
Add 4 to both sides:
Solving for
Collect in terms of x and add to both sides:
Divide both sides by e-2:
The solutions are:
If we evaluate x=4 in the original equation:
This is an absurd because log (x) is undefined for
If we evaluate in the original equation:
Which is correct, therefore the solution is: