Question

Evaluate the expression when $x=-5,y=14,\text{and}z=-7$.

$z-y-x$

Short answer

The value of the expression is $-16$.

Step-by-step solution

Step 1. Apply the concept of subtraction

To add two numbers with similar signs, add their absolute values and keep the similar sign with the resulting number.

To add two numbers with opposite signs, subtract the absolute value of smaller number from absolute value of larger number and keep the sign of larger number with the resulting number.

Step 2. Example for subtraction of numbers

The difference of the numbers $7-3=4$ is positive because the larger number is positive.

And the difference of the numbers $3-7=-4$ is negative because the larger number is negative.

Step 3. Evaluate the expression

To evaluate the expression $z-y-x$, substitute – 5 for x, 14 for y, and – 7 for z in the given expression to get

$z-y-x=-7-14-\left(-5\right)$

Now to simplify further, find the difference of first two numbers and then subtract the last number from the resulting difference of first two numbers.

To subtract \[14\], add its opposite $-14$ with first number and solve as follows

$\begin{array}{c}-7-14-\left(-5\right)=-7+\left(-14\right)-\left(-5\right)\\ =-21-\left(-5\right)\end{array}$

Now, to subtract $-5$, add its opposite $5$and solve as follows

$\begin{array}{c}-7-14-\left(-5\right)=-21-\left(-5\right)\\ =-21+5\\ =-16\end{array}$

Thus, the value of the expression is $-16$.