Chapter 1.2, Problem 14WE

a.

To determine

To Evaluate: The expression $zt-y$ if $t=6$ , $x=3$ , $y=4$ , and $z=5$

Answer to Problem 14WE

The value of the expression $zt-y$ is $zt-y=26$

Explanation of Solution

Given information:

The expression $zt-y$ and the values $t=6$ , $x=3$ , $y=4$ , and $z=5$

Concept Used:

The value of an expression at the given values of the unknowns is calculated by substituting the given values of the unknowns into the expression and simplifying it.

Calculation:

Given the expression $zt-y$

Evaluating the expression $zt-y$ at $z=5$ , $t=6$ , and $y=4$ , we have

  $\begin{array}{c}zt-y=\left(5\right)\left(6\right)-4\text{ Substituting } z=5\text{, }t=6\text{, }y=4\\ =30-4\text{ Multiplying}\\ =26\text{ Subtracting}\end{array}$

Therefore, $zt-y=26$

Conclusion:

The value of the expression $zt-y$ is $zt-y=26$

b.

To determine

To Evaluate: The expression $z\left(t-y\right)$ if $t=6$ , $x=3$ , $y=4$ , and $z=5$

Answer to Problem 14WE

The value of the expression $z\left(t-y\right)$ is $z\left(t-y\right)=10$

Explanation of Solution

Given information:

The expression $z\left(t-y\right)$ and the values $t=6$ , $x=3$ , $y=4$ , and $z=5$

Concept Used:

The value of an expression at the given values of the unknowns is calculated by substituting the given values of the unknowns into the expression and simplifying it.

Calculation:

Given the expression $z\left(t-y\right)$

Evaluating the expression $z\left(t-y\right)$ at $z=5$ , $t=6$ , and $y=4$ , we have

  $\begin{array}{c}z\left(t-y\right)=5\left(6-4\right)\text{ Substituting } z=5\text{, }t=6\text{, }y=4\\ =5\left(2\right)\text{ Multiplying}\\ =10\text{ Subtracting}\end{array}$

Therefore, $z\left(t-y\right)=10$

Conclusion:

The value of the expression $z\left(t-y\right)$ is $z\left(t-y\right)=10$