This GSEB Class 7 Maths Notes Chapter 4 Simple Equations covers all the important topics and concepts as mentioned in the chapter.
Simple Equations Class 7 GSEB Notes
1. Constant: A quantity which takes a fixed numerical value is called a constant.
For example: 4, 7, – \(\frac{1}{2}\) are constants.
2. Variable: The word variable means something that can vary; i.e. change. A variable in algebra takes on different numerical values; the value of a variable is not fixed.
3. Variables are usually denoted by letters of alphabet such as x, y, z, l, m n, p etc.
Expression: From variables we form expression. The expressions are performed by performing operations like addition, subtraction, multiplication and division on variables.
For example:
5x + 3 is an expression in which first we multiply variable x by 5 and then add 3 to proved.
4. Value of an expression: The value of an expression depends upon the value of variable from which the expression is formed.
For example:
- When x = 6; 5x + 3 = 5 × 6 + 3 = 30 + 3 = 33
- When x = 0; 5x + 3 = 5 × 0 + 3 = 0 + 3 = 3 and so on.
5. Equation: Equation is a kind of condition on a variable. In an equation there is always an equality sign. The equality sign shows that value of expression to the left of sign (or L.H.S.) is equal to the value of expression to the right of the sign (or R.H.S.)
For example:
- 5x + 3 = 33 is an equation.
- 5x + 3 > 33 is not an equation.
- 5x + 3 < 33 is not an equation.
Note:
- Atleast one of the two expressions must contain the variable.
- An equation remains the same, when the expression on the left and on the right are interchanged. This property is often useful in solving equations.
6. Solution of an equation: A number, which when substituted for a variable in an equation makes L.H.S. = R.H.S. is said to satisfy the equation and is called a solution of the equation.
For example:
x = 3 is the solution of equation 2x – 5 = 1 because L.H.S = 2x – 5
=2 × 3 – 5 = 6 – 5 = 1 = R.H.S.
7. Trial and Error method to find the solution of equation: In this method, we often make a guess of the solution of the equation. We find the values of L.H.S. and R.H.S. of the given equation for different values of the variable. The value of the variable for which L.H.S. = R.H.S. is solution of the equation.
Linear Equation
If in an equation of one variable, the highest power of the variable is 1, the equation is called a linear equation in one variable.
- The equations 2y + 6 = 7, p = \(\frac{7}{2}\), 2q + 10 = 0 are all linear equations in one variable.
- The equations 3x2 + 2x + 6 = 0 and 2x2 = 8 are not linear equations.
Formation of an Equation
- Step 1. Read the problem carefully and identify the unknown quantity or quantities.
- Step 2. Denote the unknown quantities by x, y, z, ……….. or a, b, c, ………… etc.
- Step 3. Write the given statements in the form of expressions using mathematical symbols like, +, x and ÷.
- Step 4. Write the equation by equating the expressions according to the given problem.
Solving An Equation (By Balancing)
Consider the equation x + 4 = 6, we shall subtract 4 from both sides of this equation. The new LHS (left hand side) will be x + 4 – 4 = x.
In the same way the new RHS will be 6 – 4 = 2 Hence LHS and RHS are still balanced (not changed), i.e. x = 2
Rules for solving an equation:
- The same quantity can be added to both the sides of an equation without disturbing the balance.
- The same quantity can be subtracted from both the sides of an equation without disturbing the balance.
- Both the sides of an equation may be multiplied by the same non-zero number without disturbing the balance.
- Both the sides of an equation may be divided by the same non-zero number without disturbing he balance.
- If we fail to do the same mathematical operation on both sides of an equation, the equality does not hold.
Remember
Sometimes, we may have to carryout more than one mathematical opeation for solving an equation. We should make an attempt that the variable in the equation gets separated.
Application of Simple Equations to Practical Situations
Due to the wide variety of word (or applied) problems, there is no single technique that works in all problems. However, the following general suggestion may prove helpful.
- Read the statement of the problem carefully and determine what quantity must be found.
- Represent the unknown quantity by a letter.
- Determine which expressions are equal and write an equation.
- Solve the resulting equation.