Without Using A Calculator Find X 3 X 2

This guide explains how to solve for x in the equation 3x = 2 without using a calculator. We'll cover the step-by-step process, the formula used, and provide a calculator for quick reference.

How to Find x in 3x = 2

Solving for x in the equation 3x = 2 is a fundamental algebra problem. The goal is to isolate x on one side of the equation. Here's how to do it without a calculator:

Formula: x = 2 / 3

The solution involves dividing both sides of the equation by 3 to isolate x. This basic algebraic operation is the foundation for solving more complex equations.

Step-by-Step Guide

Start with the equation: 3x = 2
Divide both sides by 3: (3x)/3 = 2/3
Simplify: x = 2/3

Remember that dividing both sides of an equation by the same non-zero number maintains the equality. This is a fundamental property of equations.

Formula

The general formula for solving equations of the form ax = b is:

x = b / a

In our specific case, a = 3 and b = 2, so x = 2 / 3.

Example

Let's work through an example to see how this applies in practice.

Example Problem: Solve for x in 3x = 2.

Solution:

Start with 3x = 2
Divide both sides by 3: x = 2/3

The value of x is 2/3 or approximately 0.6667 when expressed as a decimal.

FAQ

What if the equation has a different coefficient?

The same method applies. For any equation of the form ax = b, you divide both sides by a to solve for x.

Can I solve for x if the equation is more complex?

Yes, but the method is similar. You'll need to isolate x by performing operations that maintain the equality of both sides.

What if the coefficient is negative?

The process is the same. For example, in -3x = 2, you would divide both sides by -3 to get x = -2/3.