Algebra 2 kicks off with linear functions and equations, which...
Algebra 1334 views·Updated Jul 12, 2026·1 pageUnderstanding Linear Equations in One Variable: A Study Guide
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Solving Linear Equations in One Variable
Linear equations can be written in the form ax + b = c, where x is the variable you're solving for, and a, b, and c are just numbers. Your goal is to find the value of x that makes the equation true.
The number of solutions depends on the value of a. When a isn't zero, you'll get exactly one solution. But if a equals zero, things get interesting - you'll either have no solution (when b ≠ c) or infinitely many solutions , which we call an identity.
💡 When solving equations, remember you're using the addition and multiplication properties of equality - whatever you do to one side, you must do to the other!
Let's see this in action with examples:
Example 1: To solve 8x - 12 = 3x + 7, first group like terms by subtracting 3x from both sides to get 5x - 12 = 7. Add 12 to both sides: 5x = 19. Finally, divide by 5 to find x = 3.8.
Example 2: For 4x - 2 = 3 + 5, start by distributing: 4x - 2x - 12 = 6x + 21 + 5. Simplify to 2x - 12 = 6x + 26, subtract 2x from both sides, then subtract 26 from both sides. You'll get -38 = 4x, so x = -9.5.
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Algebra 1334 views·Updated Jul 12, 2026·1 pageUnderstanding Linear Equations in One Variable: A Study Guide
sav@s8atvika
Algebra 2 kicks off with linear functions and equations, which are foundational skills you'll use throughout math. In this chapter, we'll explore how to solve equations with one variable, understand different types of solutions, and apply key properties to find...
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Solving Linear Equations in One Variable
Linear equations can be written in the form ax + b = c, where x is the variable you're solving for, and a, b, and c are just numbers. Your goal is to find the value of x that makes the equation true.
The number of solutions depends on the value of a. When a isn't zero, you'll get exactly one solution. But if a equals zero, things get interesting - you'll either have no solution (when b ≠ c) or infinitely many solutions , which we call an identity.
💡 When solving equations, remember you're using the addition and multiplication properties of equality - whatever you do to one side, you must do to the other!
Let's see this in action with examples:
Example 1: To solve 8x - 12 = 3x + 7, first group like terms by subtracting 3x from both sides to get 5x - 12 = 7. Add 12 to both sides: 5x = 19. Finally, divide by 5 to find x = 3.8.
Example 2: For 4x - 2 = 3 + 5, start by distributing: 4x - 2x - 12 = 6x + 21 + 5. Simplify to 2x - 12 = 6x + 26, subtract 2x from both sides, then subtract 26 from both sides. You'll get -38 = 4x, so x = -9.5.
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