Question

Simplify: $19-|11-4(3-1\left)\right|$.

Short answer

The simplified value is 16.

Step-by-step solution

Step 1. Given Information: 

Consider the given expression,

$19-\left|11-4\left(3-1\right)\right|$

Step 2. Perform Subtraction:

Start with the innermost grouping symbol, which is parentheses in this case. Subtract 1 from 3 inside the parentheses.

$19-\left|11-4\left(2\right)\right|$

Step 3. Perform Multiplication:

Multiply 4 by 2.

$19-\left|11-8\right|$

Step 4. Perform subtraction:

Subtract 8 from 11 inside the absolute value bars.

$19-\left|3\right|$

Step 5. Simplify the absolute value:

Since 3 is a positive number, the absolute value of 3 is 3, that is, $\left|3\right|=3$. Write 3 for $\left|3\right|$.

$19-3$

Step 6. Simplification:

Subtract 3 from 19.

$19-3=6$

Step 7. Conclusion:

The simplified value of $19-\left|11-4\left(3-1\right)\right|$is 16.