Solve the inequality: $$ 4|m-5|-4

Question

Solve the inequality: $$ 4|m-5|-4<20 $$

UpStudy AI · Accepted Answer

To solve the inequality $$ 4|m - 5| - 4 < 20 $$, follow these steps:

1. **Isolate the absolute value term:**
   
   $$
   4|m - 5| - 4 < 20
   $$
   
   Add 4 to both sides:
   
   $$
   4|m - 5| < 24
   $$

2. **Divide both sides by 4 to simplify:**
   
   $$
   |m - 5| < 6
   $$

3. **Interpret the absolute value inequality:**

The inequality $$ |m - 5| < 6 $$ means that the expression inside the absolute value is less than 6 units away from 0. This can be rewritten as a compound inequality:

$$
   -6 < m - 5 < 6
   $$

4. **Solve for $$ m $$:**
   
   Add 5 to all parts of the inequality:
   
   $$
   -6 + 5 < m < 6 + 5
   $$
   
   $$
   -1 < m < 11
   $$

**Solution:**

All real numbers m with m greater than –1 and less than 11.

In interval notation:
$$ -1 < m < 11 $$
The solution to the inequality $$ 4|m - 5| - 4 < 20 $$ is all real numbers $$ m $$ such that $$ -1 < m < 11 $$.

Solve the inequality:

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