to view answer.To evaluate an expression means to find the value of the expression when the variables in the expression are replaced with specific values. It is very important when evaluating expressions to follow the order of operations.
Evaluate the following expression when $$x=7$$:
\[{\frac{x^2+(4-2x)\;}{x+3}}\]
1. To evaluate the expression when $$x=7$$, replace each x in the expression with the value of 7:
\[{\frac{x^2+(4-2x)\;}{x+3}}={\frac{7^2+(4-2 \cdot 7)\;}{7+3}}\]
2. Now, following the order of operations, perform the operations inside parentheses first. In this problem, it appears that there is only one set of parentheses. However, since the expression $$7^2+(4-2 \cdot 7)$$ is divided by the expression $$7+3$$, it is important to simplify the numerator seperately from the denominator.
\[{\frac{7^2+(4-2 \cdot 7)\;}{7+3}}={\frac{[7^2+(4-2 \cdot 7)]\;}{[7+3]}}\]
3. Next, simplify the numerator and denominator. It does not matter which you simplify first, as long as they are both simplified before performing the division operation between them. Beginning by examining the numerator separately, we have:
\[7^2+(4-2 \cdot 7)\]
Here, follow the order of operations within the numerator, and simplify inside the parentheses first. Within these parentheses, we still need to follow the order of operations, so we multiply first, then subtract:
\[{\frac{\left[7^2+(4-2 \cdot 7)\right]}{\left[7+3\right]}}={ \frac{\left[7^2+(4-14)\right]}{\left[7+3\right]}}= {\frac{\left[7^2+(-10)\right]}{\left[7+3\right]}}\]
4. To finish the simplifying the numerator, follow the order of operations again by first squaring the 7 and then adding -10:
\[{\frac{\left[7^2+(-10)\right]}{\left[7+3\right]}}={ \frac{\left[49+(-10)\right]}{\left[7+3\right]}}= {\frac{39}{\left[7+3\right]}}\]
5. Finally, we simplify the denominator, by adding 7+3.
\[{\frac{39}{\left[7+3\right]}}={\frac{39}{10}}\]
6. The final answer can be written in a few forms,which are all equivalent and accurate:
\[{\frac{39 \;}{10}}=3{\frac{9}{10}}=3.9\]
This is the result of the original expression evaluated for $$x=7$$.
[Note that a decimal answer is only accurate if you can write all of its digits, as in this problem. When you round a decimal answer, it is only an approximation.]
Check your skills by completing the following problems:
1. Evaluate the following expression when x = 3.
$${\Large\frac{x + 3x^2 - (x + 3)\;} {x + 9}}$$
Think about it for a moment and then access this link to view answer.
2. Evaluate the following expressions when x = 5.
$$\eqalign{
& a)\;\;\;(x - 2)^2 + x - 3(x + 1) \cr
& b)\;\;\;\;x^2 - 6x + 1 \cr} $$
Think about it for a moment and then access this link to view answer.
3. Evaluate the following expression when x = 2 and y = 3.
$${\Large{{(x + 2)^3 + 2y - 6xy + 3x \;} \over {2x + 4y}}}$$
Think about it for a moment and then access this link to view answer.
4. Evaluate the following expression when x = 0 and y = 2
$${\Large{{3x + 3 - 3(x + 1) - xy + y \;} \over {x + 1}}}$$
Think about it for a moment and then access this link to view answer.
5. Evaluate the following expression when x = 3 and y = 1.
$${\Large {{x + y(x^2 + x - 3) - 9 - x^2y - xy - 3y \;} \over {12 + x}}}$$
Think about it for a moment and then access this link to view answer.