Solve: If 3x + 2 = 11, find x.

Solving Simple Algebraic Equations: A Step-by-Step Guide

Ever needed to quickly calculate a discount at a sale or figure out how to split a bill evenly? That's algebra in action! Algebra might sound intimidating, but solving basic equations is simpler than you think. This guide shows you exactly how to solve a common type of equation: 3x + 2 = 11.

Deconstructing 3x + 2 = 11

Let's break down what this equation means. It's like a puzzle where we need to find the value of 'x'.

  • 3x: This means 3 times x. 'x' is a variable – a letter representing an unknown number.
  • +: This is the addition symbol.
  • 2: This is a constant – a fixed number.
  • =: This is the equals sign. It shows that both sides of the equation have the same value.
  • 11: This is another constant.
  • 3: This is the coefficient of 'x', indicating the multiplier of the variable.

Isolating the Variable – Step-by-Step Solution

Our goal is to find the value of 'x'. To do this, we need to 'isolate' it, meaning get 'x' by itself on one side of the equals sign.

Step 1: Subtracting the Constant

First, let's get rid of the '+2'. To do this, we subtract 2 from both sides of the equation. This keeps the equation balanced:

3x + 2 - 2 = 11 - 2

This simplifies to:

3x = 9

Step 2: Dividing by the Coefficient

Now, we have 3 times x equals 9. To find 'x', we divide both sides of the equation by 3:

3x / 3 = 9 / 3

This gives us:

x = 3

Step 3: Verifying the Solution

Let's check if our answer is correct. We substitute x = 3 back into the original equation:

3(3) + 2 = 11

9 + 2 = 11

11 = 11

The equation is true! Therefore, our solution, x = 3, is correct.

Test Your Skills

Try solving these equations:

  1. 2x + 5 = 9
  2. 4x - 3 = 9
  3. 5x + 2 = 17

Answers: 1) x = 2, 2) x = 3, 3) x = 3

Mastering Basic Algebra

Solving simple algebraic equations involves isolating the variable by performing the same operation on both sides of the equation. Remember to always check your answer! With practice, you'll become proficient in solving these equations, a skill that's valuable in many areas of life and further mathematical studies.

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