Solve the compound inequality.
<−16<−2x4−4
Graph the solution on the number line.
-3<2x+3<9
To solve the compound inequality <-16 < -2x + 4 < -4, we need to isolate the variable x within the inequality. Here's how to do it step by step:
Step 1: Solve the first inequality: -16 < -2x + 4
To isolate x, subtract 4 from both sides:
-16 - 4 < -2x + 4 - 4
-20 < -2x
Step 2: Divide both sides of the inequality by -2, remembering to flip the inequality sign since we are dividing by a negative number:
(-20) / (-2) > x
10 > x
Step 3: Solve the second inequality: -2x + 4 < -4
To isolate x, subtract 4 from both sides:
-2x + 4 - 4 < -4 - 4
-2x < -8
Step 4: Divide both sides of the inequality by -2, remembering to flip the inequality sign:
(-2x) / (-2) > (-8) / (-2)
x > 4
So, the solution to the compound inequality is 10 > x > 4.
To graph the solution on a number line, draw a line and mark it with numbers that include the range stated in the solution. In this case, label the number line with numbers between 10 and 4 (excluding 10 and 4 themselves), since x should be greater than 4 but less than 10. You can represent this on a number line as an open circle at 10 and an open circle at 4 with a line segment in between.
Here is a visual representation of the solution on a number line:
x
----------o----o--------
4 10