What you need
- A pencil and paper
- The linear equation to solve (e.g., 3x + 5 = 14)
- A calculator (optional)
- Basic knowledge of algebraic operations
Every step
- 1
Identify the variable and terms
Locate the variable (usually x or y) in the equation. Write down the equation clearly, for example: 3x + 5 = 14. Identify all numbers and variable terms on each side. This helps in the organization of following steps.
CHECKPOINT · Equation written with variable and terms marked. - 2
Isolate variable terms on one side
Move all terms containing the variable to one side and constants to the other. For 3x + 5 = 14, subtract 5 from both sides: 3x + 5 - 5 = 14 - 5, simplifying to 3x = 9.
CHECKPOINT · Only variable terms remain on one side (e.g., 3x = 9). - 3
Solve for the variable
Divide both sides by the coefficient of the variable. In the example 3x = 9, divide both sides by 3: (3x)/3 = 9/3, which results in x = 3.
CHECKPOINT · Variable isolated (e.g., x = 3). - 4
Check your solution
Substitute your solution back into the original equation: 3x + 5 = 14 becomes 3*3 + 5 = 14, which is 9 + 5 = 14. If the numbers balance, your solution is correct.
CHECKPOINT · Original equation is true when the solution is plugged in. - 5
Handle a fraction without changing the equation
For x/2 + 1 = 5, first subtract 1 from both sides to get x/2 = 4. Multiply both sides by 2 to get x = 8. Check: 8/2 + 1 = 5. Clearing fractions is another option, but multiply every term on both sides by the chosen denominator.
CHECKPOINT · The substituted value makes the original equation true.
Common mistakes
- When multiplying or dividing by a negative, double-check the sign.
- Mixing up steps can lead to incorrect solutions; work methodically.
Finished when
You have an explicit value for the variable and verified it by substitution.
Questions about this task
What if the equation has variables on both sides?
Move all variable terms to one side and constant terms to the other. Combine like terms, then solve as usual. For example, with 2x + 3 = x + 5, subtract x from both sides to get x + 3 = 5, then continue solving.
How should I handle negative coefficients?
If the variable has a negative coefficient, divide both sides by the negative number. For example, with -2x = 4, divide by -2 to get x = -2.
Make these steps fit your situation.
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