Question

In the following exercises, simplify each expression.

$9-3\left|2\left(2-6\right)-\left(3-7\right)\right|$

Short answer

$-3$

Step-by-step solution

Step 1. Given Information

The given expression is$9-3\left|2\left(2-6\right)-\left(3-7\right)\right|$.

Step 2. Simplify the expression inside the absolute bar.  

• Remove the brackets first by subtracting 6 from 2 and subtracting 7 from 3.

$9-3\left|2\left(2-6\right)-\left(3-7\right)\right|=9-3\left|2\left(-4\right)-\left(-4\right)\right|$

• Apply the order of operation. Perform multiplication operations.

$9-3\left|2\left(-4\right)-\left(-4\right)\right|=9-3\left|-8+4\right|$

• Add $-8$and 4.

$9-3\left|-8+4\right|=9-3\left|-4\right|$

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.

$9-3\left|-4\right|=9-3\left(4\right)$

• Simplify by performing multiplication operation first.

$\begin{array}{rcl}9-3\left(4\right)& =& 9-12\\ & =& -3\end{array}$

Step 4. Conclusion

The resultant value is$-3$.