Follow The Steps To Finish Solving The Equation \[$-3x = 10\$\].1. Add \[$3x\$\] To Both Sides To Isolate The Variable Term: \[$-3x + 3x = 10 + 3x\$\].2. Divide Both Sides By 10: $\[x = \frac{10}{3}.\\]\[$x =\
**Solving Linear Equations: A Step-by-Step Guide** =====================================================
Understanding Linear Equations
A linear equation is an algebraic equation in which the highest power of the variable(s) is 1. It is a simple equation that can be solved using basic algebraic operations. In this article, we will focus on solving linear equations of the form ax = b, where a and b are constants.
Step 1: Isolate the Variable Term
To solve a linear equation, we need to isolate the variable term. This means we need to get the variable term by itself on one side of the equation. In the equation -3x = 10, we need to add 3x to both sides to isolate the variable term.
Step 2: Add 3x to Both Sides
Adding 3x to both sides of the equation -3x = 10 gives us:
-3x + 3x = 10 + 3x
This simplifies to:
0 = 10 + 3x
Step 3: Subtract 10 from Both Sides
Subtracting 10 from both sides of the equation 0 = 10 + 3x gives us:
0 - 10 = 10 + 3x - 10
This simplifies to:
-10 = 3x
Step 4: Divide Both Sides by 3
Dividing both sides of the equation -10 = 3x by 3 gives us:
(-10) / 3 = 3x / 3
This simplifies to:
-10/3 = x
Solving the Equation
Therefore, the solution to the equation -3x = 10 is x = -10/3.
Q&A
Q: What is a linear equation? A: A linear equation is an algebraic equation in which the highest power of the variable(s) is 1.
Q: How do I isolate the variable term in a linear equation? A: To isolate the variable term, you need to add or subtract the same value from both sides of the equation.
Q: What is the first step in solving a linear equation? A: The first step in solving a linear equation is to isolate the variable term.
Q: How do I solve the equation -3x = 10? A: To solve the equation -3x = 10, you need to add 3x to both sides, then subtract 10 from both sides, and finally divide both sides by 3.
Q: What is the solution to the equation -3x = 10? A: The solution to the equation -3x = 10 is x = -10/3.
Common Mistakes to Avoid
- Not isolating the variable term
- Not adding or subtracting the same value from both sides
- Not dividing both sides by the correct value
Conclusion
Solving linear equations is a fundamental concept in algebra. By following the steps outlined in this article, you can easily solve linear equations of the form ax = b. Remember to isolate the variable term, add or subtract the same value from both sides, and finally divide both sides by the correct value. With practice, you will become proficient in solving linear equations and be able to tackle more complex algebraic equations.
Additional Resources
- Khan Academy: Linear Equations
- Mathway: Linear Equations
- Algebra.com: Linear Equations
Practice Problems
- Solve the equation 2x = 12
- Solve the equation x/2 = 3
- Solve the equation 4x = 20
Answer Key
- x = 6
- x = 6
- x = 5