Section 1.7: Using Variables and Formulas Worksheet 1.7
Definition: A variable is a letter which represents and unknown number.
People use lots of different symbols for variables, for example: $x$, $y$, $z$, $a$, $b$, $c$, $\alpha$, $\beta$,
$\gamma$, $\xi$, $\theta$, and so on.
Definition: An expression containing variables is called an algebraic expression.
Example: $$\frac{xy-\sqrt{z}}{\alpha}$$ is an example of an algebraic expression.
Evaluating Algebraic expressions. When we put actual numbers in for the variables in an algebraic expression,
we evaluate the algebraic expression.
Example: Evaluate the expression $$\frac{xy-\sqrt{z}}{\alpha}$$ for $x=-1$, $y=3$, $z=9$, $\alpha=7$
Application: wants to build a round house with a radius of 20 feet.
How far will it be to walk around the house?
Hint: Use the formula $C=2\pi r$ to calculate the circumference.
Application:
An automobile lease requires an
initial payment of $\$$1,000 followed by monthly
payments of $\$$400 for 2 years. The equation
$a_n = 400n + 1,000$ gives the total of all payments
made on this lease after $n$ months. Use this equation to
calculate the total paid after each of the first 3 months.
Equations and their Solutions
A value which makes an equation a true statement is called a solution to the equation.
Example: The value $b=-2$ is not a solution to the equation $b^2+2b-3=0$, but $b=1$ is a solution.