Question

Find the value of each expression

$1-\left\{30÷\left[7+3\left(-4\right)\right]\right\}$

Short answer

Value of$1-\left\{30÷\left[7+3\left(-4\right)\right]\right\}$ is 7

Step-by-step solution

- Order for simplification 

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) , brackets [ ] or braces { }.
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

- Simplify expression inside grouping symbol

To evaluate the value of the given expression, first simplify the expression inside the parenthesis and then simplify the expression inside braces as shown below

$\begin{array}{c}1-\left\{30÷\left[7+3\left(-4\right)\right]\right\}=1-\left\{30÷\left[7+\left(-12\right)\right]\right\}\\ =1-\left\{30÷\left(-5\right)\right\}\\ =1-\left(-6\right)\end{array}$

- Subtract from 1

Now, to simplify further subtract the numbers to get

$1-\left\{-6\right\}=7$

Thus, value of$1-\left\{30÷\left[7+3\left(-4\right)\right]\right\}$ is 7