6th Grade - Introductions to Equations

Introduction

• An equation is a mathematical statement that shows that two expressions are equal.
• Examples:, $2y=6$, $3m-9=12$, etc.
• All the equations have an equal sign (=).
• An equation is said to be linear if it contains only one variable with the highest power of 1 (one).

Solving simple linear equations

• The value of the variable for which the equation is satisfied is called the solution of the equation.
• In order to solve an equation, perform the following steps as applicable:

• • Combine like terms
  • Solve using the addition principle
  • Solve using the subtraction principle
  • Solve using the multiplication principle
  • Solve using the division principle

Solved Examples

Question 1: Solve the following equation.

$x+3=1$

Solution: $x+3=1$

Applying the subtraction rule.

$x+3-3=1-3$

$x=-2$

 

Question 2: Solve the following equation.

$m-2=5$

Solution: $m-2=5$

Applying the addition rule.

$m-2+2=5+2$

$m=7$

 

Question 3: Solve the following equation.

$\frac{x}{2}=4$

Solution: $\frac{x}{2}=4$

Apply the multiplication rule.

$\frac{x}{2}\times 2=4\times 2$

$x=8$

 

Question 4: Solve the following equation.

$7x=21$

Solution: $7x=21$

Apply the division rule.

$\frac{7x}{7}=\frac{21}{7}$

$x=3$

Cheat Sheet

• A mathematical statement that has two expressions separated by an equality sign is called an equation.
• An equation remains the same if its LHS and RHS are interchanged.
• The value of a variable for which the equation is satisfied is called the solution of the equation.

Blunder Areas

• Whatever operation you do on one side of the equation, perform the same operation on the other side as well.
• Pay close attention to the signs while performing any operation with negative numbers.

Solving simple linear inequalities (to be deleted)

• Inequalities can be solved using the rules mentioned below.

• • Adding the same number to each side of an inequality produces an equivalent inequality wherein the sign of inequality remains unaffected.
  • Subtracting the same number from both sides of an inequality results in an equivalent inequality wherein the sign of inequality remains unaffected.
  • Multiplying both sides of an inequality by a positive number results in an equivalent inequality wherein the sign of inequality remains unaffected.
  • Multiplying both sides of an inequality by a negative number results in a new inequality wherein the sign of inequality is reversed.
  • Dividing both sides of an inequality by a positive number results in an equivalent inequality wherein the sign of inequality remains unaffected.
  • Dividing both sides of an inequality by a negative number results in a new inequality wherein the sign of inequality is reversed.