Download on Solving Linear Equations

Elementary Algebra Notes
Section 2.3
Page 1 of 2
Section 2.3: More on Solving Linear Equations
Big Idea: There are four basic steps to solving linear equations.
Definition of a Linear Equation: A linear equation (after simplification) has only numbers and the variable to
the first power. Algebraic description of a linear equation: Ax + B = C, and A  0.
Steps for solving a linear equation:
1. Simplify each side separately.
a. Use the distributive property to remove parentheses.
b. Combine like terms.
2. Isolate the variable term.
a. Use the addition property of equality to get all variable terms on one side.
b. Use the addition property of equality to get all numbers on the other side.
3. Isolate the variable.
a. Use the multiplication property of equality to get: x = a number.
4. CHECK YOUR WORK!!
Examples:
 12t  7  3t  9  20

8t 10 10t  9  2  2t  3

3
1
 y  7   2 y  4  y
4
8
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra Notes
Section 2.3
Page 2 of 2

Suppose that you are planning a party, and that you assume each guest will drink 5 sodas. If you want at
least 12 sodas leftover, and a case of soda cost $7.99 plus tax, find out how many guests you can invite
to your party if you can only spend $50 on soda.

Suppose you are planning a wedding, and the reception hall costs a flat fee of $500 plus $15 per guest
for food and $30 per guest for open bar. All of this has tax added on. If you have $2,000 to spend on
the reception, how many guests can you invite?
Special situations in equation solving:
1. Sometimes an equation has NO SOLUTIONS. In this case, the variables disappear after you try to
get them all on one side, and you are left with a false number statement. That means that the equation
can’t be solved for any value of the variable.
2t + 1 = 2t
2. Sometimes an equation has INFINITELY MANY SOLUTIONS. In this case, the variables
disappear after you try to get them all on one side, but you are left with a true number statement. That
means that the equation is solved by ANY value of the variable.
5x – 15 = 5(x – 2) – 5
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.