Chapter 1.3, Problem 37IP

To determine

The value of the expression $\left(29-3y\right)+4z-7$ .

Answer to Problem 37IP

  $58$

Explanation of Solution

Given information:

The values: $x=9,y=4,\text{and }z=12$ .

Concept Used:

• For Order of Operation, we will use PEMDAS rule.

Symbols are representing:

P − parenthesis, E − exponent, M − multiplication,

D − division, A − addition and S − subtraction.

• If grouping symbols such as parenthesis are present, simplify expressions within those first, starting with the innermost set.
• Evaluate exponential expressions or absolute values in order from left to right.
• Multiply or divide in order from left to right.
• Add or subtract in order from left to right.

If there is no grouping symbols or no exponents, we multiply or divide and then add or subtract in the order from left to right.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the value of the expression $\left(29-3y\right)+4z-7$ , substitute the value of y, andz and simplify further by combining the like terms as shown below

  $\begin{array}{c}\left(29-3y\right)+4z-7=\left(29-3\cdot 4\right)+4\cdot 12-7\\ =\left(29-12\right)+4\cdot 12-7\\ =\left(17\right)+4\cdot 12-7\\ =17+48-7\\ =65-7\\ =58\end{array}$

Thus, the value of the expression is $58$ .