Question

In the following exercises, simplify each expression. $5-2\left|2\left(1-4\right)-\left(2-5\right)\right|$

Short answer

$-1$

Step-by-step solution

Step 1. Given Information

The given expression is$5-2\left|2\left(1-4\right)-\left(2-5\right)\right|$.

Step 2. Simplify the expression inside the absolute bar.

• Remove the brackets first by subtracting 4 from 1 and subtracting 5 from 2.

$5-2\left|2\left(1-4\right)-\left(2-5\right)\right|=5-2\left|2\left(-3\right)-\left(-3\right)\right|$

• Apply the order of operation. Perform multiplication operations.

$5-2\left|2\left(-3\right)-\left(-3\right)\right|=5-2\left|-6+3\right|$

• Add $-6$and 3.

$5-2\left|-6+3\right|=5-2\left|-3\right|$

Step 3. Use the definition of the absolute value.  

• Since the absolute value is always greater than and equal to 0, take the absolute value of the obtained value in the previous step.

$5-2\left|-3\right|=5-2\left(3\right)$

• Simplify by performing multiplication operation first.

$\begin{array}{rcl}5-2\left(3\right)& =& 5-6\\ & =& -1\end{array}$

Step 4. Conclusion

The resultant value is$-1$.