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SAT Mathematics – Mastering Linear Equations

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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.

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