Which graph best represent following expression|x-1|>2
x - 1 > 2
x > 3
or
1 - x > 2
-x > 1
x < -1
so everything to the right of x = 3 and everything to the left of x = -1
Well, since we're talking about absolute value, let's see which graph will entertain us the most. How about we draw a whimsical curve that goes up and down, like a rollercoaster? After all, solving inequalities can be quite the thrill ride! You'll definitely find the graph of y = |x-1| > 2 captivating and amusing. Just be sure to hold on tight!
To graph the expression |x-1|>2, you will need to graph two separate inequalities.
Step 1: Graph the inequality x-1 > 2.
To do this, we need to isolate x:
x - 1 > 2
x > 2 + 1
x > 3
This means that any value of x greater than 3 will satisfy this inequality. So shade the region to the right of x = 3.
Step 2: Graph the inequality -(x-1) > 2.
Again, isolate x:
-(x - 1) > 2
-x + 1 > 2
-x > 2 - 1
-x > 1
Now, when we multiply or divide by a negative number, we need to flip the inequality sign. So, divide both sides by -1 and reverse the inequality:
x < -1
This means that any value of x less than -1 will satisfy this inequality. So shade the region to the left of x = -1.
The graph should consist of two separate regions: the region to the left of x = -1 and the region to the right of x = 3. The graph should have an open circle at x = -1 and x = 3 to indicate that these values are not included in the solution set.
To determine the graph that best represents the expression |x-1|>2, we need to first understand what this expression means.
The absolute value |x-1| represents the distance between the number x and 1 on a number line. The expression |x-1|>2 implies that the distance between x and 1 is greater than 2.
To graph this expression, we can follow these steps:
Step 1: Set up a number line.
Draw a horizontal line and mark the numbers on it. Label the number 1 on the line, as it represents the value inside the absolute value function.
Step 2: Represent the inequality symbol.
Since the expression is >2, we need to show that the distance between x and 1 is greater than 2. This means we need to shade the number line to indicate the range of values that satisfy this condition.
Step 3: Identify the solutions.
For the expression |x-1|>2, we can split it into two separate inequalities to find the range of values for x. First, we consider the case when (x-1) is positive:
x-1 > 2
Solving this inequality, we get:
x > 3
Second, we consider the case when (x-1) is negative:
-(x-1) > 2
Solving this inequality, we get:
x < -1
Step 4: Shade the appropriate regions on the number line.
Based on the two solutions from step 3, we shade the portion of the number line that falls to the right of 3 and to the left of -1. This represents all the values of x that satisfy the inequality |x-1|>2.
The resulting graph should show a shaded area to the right of 3 and a shaded area to the left of -1 on the number line.
Please note that the exact appearance of the graph may also depend on the context in which this inequality is being used.