Mastering Linear Equations: A Step-by-Step SAT Maths Guide
Introduction to Linear Equations
Linear equations form the foundation of SAT Mathematics and appear consistently in both the calculator and no-calculator sections. Whether you’re preparing in the UK, Europe, or internationally, mastering this topic is crucial for success.
This guide will explain:
- What linear equations are.
- Step-by-step strategies to solve them.
- Practice examples with solutions.
- Common mistakes to avoid.
Let’s dive in!
What is a Linear Equation?
A linear equation is any equation that can be written in the form:
\[
ax + b = c
\]
Where:
- \( a \) is the coefficient of \( x \),
- \( b \) is a constant, and
- \( x \) is the unknown variable.
Example: \( 2x + 4 = 10 \)
When graphed, linear equations form a straight line.
Step-by-Step Guide to Solving Linear Equations
Step 1: Combine Like Terms
Simplify both sides of the equation by combining like terms.
Example:
\[
3x + 2 – 1 = 11
\]
Simplify the constants:
\[
3x + 1 = 11
\]
Step 2: Isolate the Variable
Move constants to one side of the equation by adding or subtracting.
Example:
\[
3x + 1 = 11
\]
Subtract 1 from both sides:
\[
3x = 10
\]
Step 3: Solve for \( x \)
Divide both sides by the coefficient of \( x \).
Example:
\[
3x = 10 \quad \text{so} \quad x = \frac{10}{3}
\]
Practice Questions and Solutions
Question 1
Solve for \( x \):
\[
2x – 5 = 9
\]
Solution:
- Add 5 to both sides: \( 2x = 14 \).
- Divide by 2: \( x = 7 \).
Question 2
Solve for \( x \):
\[
5x + 2 = 17
\]
Solution:
- Subtract 2: \( 5x = 15 \).
- Divide by 5: \( x = 3 \).
Common Mistakes to Avoid
- Forgetting to simplify both sides first.
- Incorrect operations (sign errors when adding/subtracting).
- Skipping steps and losing track of the equation.
Quick Tips for SAT Success
- Use the process of elimination to test answer choices quickly.
- For word problems, translate text into equations.
- Double-check your work for sign errors or missteps.
Summary
Linear equations are fundamental to SAT success. Practice these steps, avoid common errors, and use strategies like elimination and backsolving to tackle these questions confidently.
Need more help with SAT Maths? Book a free consultation with Skinat Tuition to build your confidence and ace the SAT exam.
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