Math Problem Statement

teach someone SOLVING LINEAR EQUATIONS

Solution

Solving Linear Equations: A Step-by-Step Guide

Linear equations are mathematical expressions that represent a straight line when graphed. They are of the form:

ax+b=cax + b = c

where:

  • aa, bb, and cc are constants (numbers),
  • xx is the variable we need to solve for.

Steps to Solve a Linear Equation

1. Simplify Both Sides

  • If the equation has parentheses, distribute to eliminate them.
  • Combine like terms on each side of the equation.

2. Isolate the Variable

  • To get the variable (xx) on one side, we need to "undo" the operations around it by performing opposite operations (addition becomes subtraction, multiplication becomes division, etc.).

  • Start by adding or subtracting to move any constants (bb or cc) to the other side.

ax+b=cax=cbax + b = c \quad \Rightarrow \quad ax = c - b

3. Solve for the Variable

  • Once the variable term (axax) is isolated, solve for xx by dividing by the coefficient of xx (which is aa).

ax=dx=daax = d \quad \Rightarrow \quad x = \frac{d}{a}

4. Check Your Solution

  • Substitute the value of xx back into the original equation to verify that both sides are equal.

Example Problem

Solve the equation: 3x+5=143x + 5 = 14.

Step 1: Simplify Both Sides

  • The equation is already simplified.

Step 2: Isolate the Variable

  • Subtract 5 from both sides:

3x+55=1453x + 5 - 5 = 14 - 5 3x=93x = 9

Step 3: Solve for the Variable

  • Divide both sides by 3:

x=93=3x = \frac{9}{3} = 3

Step 4: Check Your Solution

  • Substitute x=3x = 3 back into the original equation:

3(3)+5=14(True!)3(3) + 5 = 14 \quad \text{(True!)}

Summary

  • Simplify both sides of the equation.
  • Isolate the variable by moving terms around.
  • Solve for the variable.
  • Check your solution.

Do you want more details on any of these steps, or do you have any questions?

Related Questions:

  1. How do you solve a linear equation with variables on both sides?
  2. What happens if a linear equation has no solution?
  3. How can you solve a linear equation with fractions?
  4. How do you solve a linear equation with decimals?
  5. What are the properties of equality used in solving equations?

Tip: Always perform the same operation on both sides of the equation to maintain the equality!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Linear equation formula ax + b = c

Theorems

-

Suitable Grade Level

Grades 7-9