Question

|4m - 4| < 36

How can you solve the absolute value inequality and graph it?
A) Subtract 4 from both sides, then divide by 4; graph the solution on a number line.
B) Add 4 to both sides, then divide by 4; graph the solution on a number line.
C) Subtract 36 from both sides, then divide by 4; graph the solution on a number line.
D) Add 36 to both sides, then divide by 4; graph the solution on a number line.

Answer 1

To solve the absolute value inequality |4m - 4| < 36, we need to consider two cases: 4m - 4 >= 0 and 4m - 4 < 0. The solution is -8 < m < 10.

Step-by-step explanation:

To solve the absolute value inequality |4m - 4| < 36, we need to consider two cases. In the first case, when 4m - 4 is greater than or equal to 0, we simply have 4m - 4 < 36. Then, we can solve this inequality by adding 4 to both sides and dividing by 4 to get m < 10. In the second case, when 4m - 4 is less than 0, we have -(4m - 4) < 36. Simplifying this inequality gives us -4m + 4 < 36. By subtracting 4 from both sides and dividing by -4, we get m > -8. Therefore, the solution to the absolute value inequality is -8 < m < 10.

Graphing this solution on a number line, we represent the range of values from -8 to 10 by shading the region between -8 and 10 but not including -8 and 10. This indicates that any value of m within this range will satisfy the inequality.