Question

Evaluate each expression if a=-5,b=6 and c=2.8

$\left|a-b\right|-\left|10c-a\right|$

Short answer

The absolute value of expression is$\mathbf{-}\mathbf{22}$

Step-by-step solution

Step1- Order of evaluation

To evaluate any expression involving one operation, follow the below order of operation

• First replace the algebraic expression inside the grouping symbols like matrix brackets ( $\left|\right|$) with numeric expression
• Perform the subtraction inside first pair of bracket

• Perform the multiplication and subtraction inside the second pair of bracket

• Evaluate the absolute values of the pair

• Perform the subtraction from left to right

Step2- Simplify the expression inside grouping symbol

To evaluate the value of given expression , simply the expression inside the bracket and then find the absolute value of expression as shown below

$\begin{array}{c}|a-b|-|10c-a|=|-5-6|-\left|10\times 2.8-(-5)\right|\\ =|-11|-|28+5|\end{array}$

Step3- Find the absolute value of expression inside the bracket and subtract

The absolute value of $\left|-11\right|=11$ and $\left|33\right|=33$

The solution is $11-33=-22$.