add 4
-2<2x<16
divide by 2
-1<x<8
-6<2x-4<12
-2<2x<16
divide by 2
-1<x<8
First, let's add 4 to all three parts of the inequality:
-6 + 4 < 2x - 4 + 4 < 12 + 4
Simplifying, we get:
-2 < 2x < 16
Next, divide each part of the inequality by 2:
-2/2 < 2x/2 < 16/2
Simplifying further:
-1 < x < 8
Now, let's graph the solution:
On a number line, draw a line from -1 to 8, and label the points -1 and 8. Shade the line between -1 and 8 to represent the numbers that satisfy the inequality -1 < x < 8. The shaded region represents the solution to the compound inequality.
Note that the endpoints, -1 and 8, are not included in the graph since the inequality is strict.
1. Solve the inequality -6 < 2x-4:
-6 < 2x-4
Add 4 to both sides: -6+4 < 2x
Simplify: -2 < 2x
Divide both sides by 2 (since the inequality is "<" and not "<="): -1 < x
2. Solve the inequality 2x-4 < 12:
2x-4 < 12
Add 4 to both sides: 2x < 16
Divide both sides by 2: x < 8
Now we have the two solutions:
-1 < x and x < 8
To graph the solution, we will plot the values of x on a number line between -1 and 8 and shade the region between these two values because it satisfies both inequalities.
Here's how to graph it:
1. Draw a number line and label it with key values including -1 and 8.
-1 8
|________|
2. Place an open circle on -1 because it doesn't include equality (<) and shade the region to the right.
-1 8
o--------|
3. Place an open circle on 8 because it doesn't include equality (<) and shade the region to the left.
-1 8
|---------o
The graph shows that x can take any value between -1 and 8, excluding -1 and 8 themselves, represented by the shaded region on the number line.