7x by 8 - 6 by 8 is equal to 3 by 5 - 9 x by 15
Answers
Step-by-step explanation:
• The word variable means something that can vary i.e., change and
constant means that does not vary. The value of a variable is not
fixed. Variables are denoted usually by letters of the English alphabets
such as x, y, z, l, m, n, p, a etc.
• The expressions are formed by performing operations like addition,
subtraction, multiplication and division on the variables and
constants.
• An equation is a condition on a variable (or variables) such that two
expressions in the variable (variables) have equal value.
• The value of the variable for which the equation is satisfied is called
the solution or root of the equation.
• An equation remains the same if the LHS and the RHS are
interchanged.
• In case of balanced equation if we (i) add the same number to both
the sides, or (ii) subtract the same number from both the sides, or
(iii) multiply both sides by the same non-zero number or (iv) divide
both sides by the same non-zero number, the balance remains
undisturbed.
• Transposing means moving from one side to the other. When a term
is transposed from one side of the equation to the other side, its sign
gets changed.
• Transposition of an expression can be carried out in the same way
as the transposition of a term.
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• To solve practical problems:
(A) Read the problem carefully and denote the unknown quantity
by variable x, y etc.
(i) Form the equation according to the given conditions.
(ii) Solve the equation i.e., find the value of the unknown
quantity (variable).
In Examples 1 to 3, there are four options, out of which one is correct.
Choose the correct one.
Example 1: The solution of the equation 3x + 5 = 0 is
(a)
5
3 (b) – 5 (c) - 5
3 (d) 5
Solution : Correct answer is (c).
Example 2: –1 is not a solution of the equation
(a) x + 1 = 0 (b) x – 1 = 2 (c) 2y + 3 =1 (d) 2p + 7 = 5
Solution : Correct answer is (b).
Example 3: Which of the following equations can be formed using
the expression x = 5:
(a) 2x + 3 = 13 (b) 3x + 2 = 13
(c) x – 5 = 1 (d) 4x – 9 =21
Solution: Correct answer is (a).
[Hint: x = 5 on multiplying both sides by 2 gives 2x = 10
which on adding 3 both sides gives 2x + 3 =13]
An equation is a mathematical sentence that uses
an equality sign to show that two expressions have
the same value. All of these are equations.
3 + 8 = 11 r + 6 = 14 – 24 = x – 7 100 – 50
2
− =
To solve an equation that contains a variable, find the value of the variable
that makes the equation true. This value of the variable is called the
solution of the equation.
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