Understand basic concepts involved in topic solving linear equations

Last Updated : 14 December 2023, Thursday

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Solution to the Equation Meaning

  • Value of the variable that makes the equation true is called solution to the equation
  • For example, 2 is the solution to equation 5x-3=7

Subtraction, addition, division,multiplication properties of equality

Subtraction Property of Equality

For all real numbers 𝑎,𝑏, and 𝑐, if 𝑎=𝑏, then 𝑎𝑐=𝑏𝑐

Addition Property of Equality

For all real numbers 𝑎,𝑏, and 𝑐, if 𝑎=𝑏, then 𝑎+𝑐=𝑏+𝑐

Division and multiplication properties of equality

properties of equalities

Translating an equation and solving

  • These words translate to Equal sign (=) :
    • is
    • is equal to
    • is the same as
    • the result is
    • gives
    • was
    • will be
  • Example : five more than x is equal to 26

General strategy to solve linear equations

Step 1. Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms.

Step 2. Collect all the variable terms to one side of the equation. Use the Addition or Subtraction Property of Equality.

Step 3. Collect all the constant terms to the other side of the equation. Use the Addition or Subtraction Property of Equality.

Step 4. Make the coefficient of the variable term to equal to 1. Use the Multiplication or Division Property of Equality. State the solution to the equation.

Step 5. Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.

Quiz

Solving Linear Equations

Questions 1 to 10 have single answer correct

1 / 10

2 / 10

3 / 10

4 / 10

5 / 10

6 / 10

Anushka and Aarushi are friends. They have equal amount of money
in their pockets. Anushka gave 1/3 of her money to Aarushi as her
birthday gift. Then Aarushi gave a party at a restaurant and cleared
the bill by paying half of the total money with her. If the remaining
money in Aarushi’s pocket is Rs.1600, find the sum gifted by
Anushka

7 / 10

Two equal sides of a triangle are each 4m less than three times the
third side. Find the dimensions of the triangle, if its perimeter is
55m.

8 / 10

Anima left one-half of her property to her daughter, one-third to her
son and donated the rest to an educational institute. If the donation
was worth Rs. 1,00,000, how much money did Anima have?

9 / 10

The perimeter of a rectangle is 240 cm. If its length is increased by
10% and its breadth is decreased by 20%, we get the same perimeter.
Find the length and breadth of the rectangle.

10 / 10

A steamer goes downstream and covers the distance between two
ports in 3 hours. It covers the same distance in 5 hours when it goes
upstream. If the stream flows at 3 km/hr, then find what is the speed
of the steamer upstream?

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The average score is 90%

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