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Concept of Equation

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definition

Equation: An equation is a condition on a variable. It is expressed by saying that expression with a variable is equal to a fixed number. e.g. x – 3 = 10.

notes

Equation:

  • An equation is a condition on a variable. It is expressed by saying that expression with a variable is equal to a fixed number. e.g. x – 3 = 10.

  • An equation has an equal sign (=) between its two sides. The equation says that the value of the left-hand side (LHS) is equal to the value of the right-hand side (RHS). If the LHS is not equal to the RHS, we do not get an equation.

  • An equation is a condition on a variable such that two expressions in the variable should have equal value.

  • 5t + 28 = 10 is an equation.

  • In an equation, there is always an equality sign. The equality sign shows that the value of the expression to the left of the sign (the left-hand side or LHS) is equal to the value of the expression to the right of the sign (the right-hand side or RHS).
    4p – 3 = 13 ( ∴ p = – 4)

  • If there is some sign other than the equality sign between the LHS and the RHS, it is not an equation. Thus, 4x + 5 > 65 is not an equation. It says that the value of (4x + 5) is greater than 65. Similarly, 4x + 5 < 65 is not an equation. It says that the value of (4x + 5) is smaller than 65.

  • An equation remains the same when the expressions on the left and on the right are interchanged.

Example

Write the following statement in the form of the equation:

The sum of three times x and 11 is 32.

Three times x is 3x.

Sum of 3x and 11 is 3x + 11. The sum is 32.

The equation is 3x + 11 = 32.

Example

Write the following statement in the form of the equation:

If you subtract 5 from 6 times a number, you get 7.

Let us say the number is z; z multiplied by 6 is 6z.

Subtracting 5 from 6z, one gets 6z – 5. The result is 7.

The equation is 6z – 5 = 7.

Example

Write the following statement in the form of the equation:

One-fourth of m is 3 more than 7.

One-fourth of m is `m/4`.

It is greater than 7 by 3. This means the difference `(m/4–7)` is 3.

The equation is `m/4` – 7 = 3.

Example

Raju’s father’s age is 5 years more than three times Raju’s age. Raju’s father is 44 years old. Set up an equation to find Raju’s age.

Let us take it to be y years. Three times Raju’s age is 3y years.
Raju’s father’s age is 5 years more than 3y; that is, Raju’s father is (3y + 5) years old. It is also given that Raju’s father is 44 years old.
Therefore, 3y + 5 =44.

This is an equation in y. It will give Raju’s age when solved.

Example

A shopkeeper sells mangoes in two types of boxes, one small and one large. A large box contains as many as 8 small boxes plus 4 loose mangoes. Set up an equation which gives the number of mangoes in each small box. The number of mangoes in a large box is given to be 100.

Let a small box contain m mangoes.
A large box contains 4 more than 8 times m, that is, 8m + 4 mangoes.

But this is given to be 100.
Thus 8m + 4 =100.

You can get the number of mangoes in a small box by solving this equation.

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Shaalaa.com | Concept of Numerical Equations & Algebraic Equations

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Concept of Numerical Equations & Algebraic Equations [00:18:36]
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