Algebra-2

To solve the inequality 10 + |3z - 4| < 16, we will follow these steps:

Step 1: Isolate the absolute value

Starting with the original inequality:

10 + |3z - 4| < 16

Subtract 10 from both sides:

|3z - 4| < 6

 

Step 2: Rewrite the absolute value inequality

The inequality |3z - 4| < 6 can be rewritten as:

-6 < 3z - 4 < 6

 

Step 3: Solve the compound inequality

Now, we will split the compound inequality into two parts:

For the left side:

3z - 4 > -6

Add 4 to both sides:

3z > -2

Divide by 3:

z >

 

For the right side:

3z - 4 < 6

Add 4 to both sides:

3z < 10

Divide by 3:

z <

 

Step 4: Combine the results

Combining both results, we have:

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