GED Math: A Simple Guide to Solving Linear Equations
Linear equations can look complicated at first, but many can be solved using a small number of consistent steps. The main goal is to isolate the variable on one side of the equation.
What Is a Variable?
A variable is a letter or symbol representing an unknown value. For example: $$ x+5=12 $$ Here, \(x\) is the unknown value. To solve the equation, determine which number makes the statement true.
Step 1: Undo Addition or Subtraction
Consider: $$ x+5=12 $$ Subtract 5 from both sides: $$ x+5-5=12-5 $$ Therefore: $$ x=7 $$ The key principle is that whatever you do to one side of an equation, you should also do to the other side.
Step 2: Undo Multiplication or Division
Consider: $$ 3x=18 $$ Divide both sides by 3: $$ \frac{3x}{3}=\frac{18}{3} $$ Therefore: x=6
Solving a Two-Step Equation
Consider: $$ 2x+6=18 $$ First subtract 6 from both sides: $$ 2x=12 $$ Then divide both sides by 2: x=6
Why Work Backward?
Equations often become easier when you reverse the operations used with the variable. If a number is added to \(x\), subtract it. If \(x\) is multiplied by a number, divide by that number. The goal is to get \(x\) by itself.
Check Your Answer
Always substitute your answer back into the original equation. Using: $$ 2x+6=18 $$ and \(x=6\): $$ 2(6)+6=18 $$ $$ 12+6=18 $$ The equation is true, so the solution is correct.
Common Mistakes
One common mistake is changing one side of an equation without making the same change to the other side. Another is performing operations in the wrong order. Students can also make simple arithmetic mistakes even when the algebraic steps are correct. Writing each step on a separate line can help prevent errors.
Practice Strategy
Start with one-step equations. Then practice:
- Two-step equations
- Equations involving negative numbers
- Equations containing fractions
- Word problems that require equations
For word problems, identify the unknown first and then translate the situation into an equation.
Final Thoughts
Linear equations become much easier when you follow a consistent process. Isolate the variable, perform the same operation on both sides, and check your answer by substituting it back into the original equation.
