Example:
Consider the equation x – 6 = –2x + 3.
To isolate the variable, we need to get all the variable terms to one side and the constant terms to the other side. Next, we combine like terms and then isolate the variable by multiplying or dividing.
Solve x – 6 = –2x + 3
Solution:
Step 1: Get all the variable terms to one side and the constant terms to the other side.
x – 6 = –2x + 3
x – 6 + 2x + 6 = –2x + 3 + 2x + 6 (Add 2x & 6 to both sides)
Step 2: Combine like terms
2x + x = 3 + 6
3x = 9
Step 3: Divide or multiply to isolate the variable
3x = 9 (Divide by 3)
x = 3
Check:
x – 6 = –2x + 3
3 – 6 = –2 • 3 + 3 (substitute x = 3 into the original equation)
–3 = –3
Example:
Consider the equation 6x – 4 = 3x + 2. To isolate the variable, we need to get all the variable terms to one side and the constant terms to the other side. Next, we combine like terms and then isolate the variable by multiplying or dividing.
Solve 6x – 4 = 3x + 2
Solution:
Step 1: Get all the variable terms to one side and the constant terms to the other side.
6x – 4 = 3x + 2
6x – 4 – 3x + 4 = 3x + 2 – 3x + 4 (Subtract 3x & add 4 to both sides)
Step 2: Combine like terms
6x – 3x = 2 + 4
3x = 6
Step 3: Divide or multiply to isolate the variable
3x = 6 (Divide by 3)
x = 2
Check:
6x – 4 = 3x + 2 (substitute x = 2 into the original equation)
6 • 2 – 4 = 3 • 2 + 2
8 = 8
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.