The value of x satisfy the equation A. 7x=4x+12
B. 2x-6-8x=x-6+4
C. 2x+3=x+4
D. 4x+5=1
Answers
Answer:
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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In Examples 4 to 6, fill in the blanks to make it a true statement.
Example 4: Any value of the variable which makes both sides of an
equation equal, is known as a ______ of the equation.
Solution: Solution
Example 5: The root of the equation y – 13 = 9 is ________.
Solution: 22
Example 6: 2x + ________ = 11 has the solution – 4.
Solution: 19
Words Numbers Algebra
You can add the same
number to both sides
of an equation, and the
statement will still be
true.
x = y implies
x + z = y + z
2 + 3 = 5
+ 4 = +4
2 + 7 = 9
In Examples 7 to 10, state whether the statements are True or False.
Example 7: 12 is a solution of the equation 4x – 5 = 3x + 10.
Solution: False
[LHS = 4 × 12 – 5 = 43
and RHS = 3 × 12 + 10 = 46 They are not equal.]
Example 8: A number x divided by 7 gives 2 can be written as
x +1
7
= 2.
Solution: False.
Example 9: x + 2 = 5 and 3x – 1 = 8 have the same solutions.
Solution: True
Example 10: The equation 3x + 7 = 10 has 1 as its solution.
Solution: True
In each of the Examples 11 to 13, form an equation for each statement.
Example 11 : One fourth of a number is 20 less than the number itself.
Solution : Let the number be x.
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So, one fourth of the number is 4
x .
x
4 is 20 less than the number itself. So, the required
equation is
4
x
= x – 20.
Example 12 : On subtracting 13 from 3 times of a number, the result
is 8.
Solution : Let the number be x.
So, 3 times the number = 3x
On subtracting 13 from it, we get 3x –13.
Therefore, 3x – 13 = 8 is the required equation.
Example 13 : Two times a number increased by 5 equals 9.
Solution : Let the required number be x.
So, 2 times this number = 2x
When increased by 5, it gives the expression 2x + 5
Thus, required equation is 2x + 5 = 9.
Example 14 : 9 added to twice a number gives 13. Find the number.
Solution : Let the number be x.
As per the given condition,
2x + 9 = 13
or 2x = 4
or x = 2
Example 15 : 1 subtracted from one third of a number gives 1. Find
the number.
Solution : Let the number be x.
According to the given condition,
1
3 x – 1 = 1
or
1
3 x = 1 + 1
or
1
3 x = 2 or x = 6.
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Example 16: Correct the incorrect equation written in Roman