Definition of a Linear Equation :
A linear equation in one variable is an equation that has one unknown.
It can be written in the form,
ax + b = 0
(where a and b are real numbers and a ≠ 0)
To solve linear equations with one unknown, we have to be aware of inverse operations.
Problem 1 :
If
3x - 4(64 - x) = 10
then the value of x is
(a) -266 (b) 133 (c) 66.5 (d) 38
Solution :
3x - 4(64 - x) = 10
3x - 256 + 4x = 10
By combining the like terms.
3x + 4x = 10 + 256
7x = 10 + 256
7x = 266
x = 266/7
x = 38
Therefore, the value of x is 38.
Problem 2 :
If
8x - 3 = 25 + 17x, then x is
(a) a fraction (b) an integer
(c) a rational number (d) cannot be solved
Solution :
Given, 8x - 3 = 25 + 17x
By combining the like terms,
8x - 17x = 25 + 3
-9x = 28
x = 28/9
Therefore, the value of x is a fraction.
Problem 3 :
The value of x for which the expressions 3x - 4 and 2x + 1 become equal is
(a) -3 (b) 0 (c) 5 (d) 1
Solution :
3x - 4 = 2x + 1 ----(1)
By combining the like terms.
3x - 2x = 4 + 1
x = 5
We have, x = 5
By applying x = 5 in equation (1), we get
3x - 4 = 2x + 1
3(5) - 4 = 2(5) + 1
15 - 4 = 10 + 1
11 = 11
So, it becomes equal.
Therefore, the value of x is 5.
Problem 4 :
8x - 7 - 3x = 6x - 2x - 3
Solution :
8x - 7 - 3x = 6x - 2x - 3
By combining the like terms.
8x - 3x - 6x – 2x = 7 - 3
-x = 4
x = -4
Therefore, the value of x is -4.
Problem 5 :
10x - 5 - 7x = 5x + 15 - 8
Solution :
10x - 5 - 7x = 5x + 15 - 8
By combining the like terms.
10x – 7x – 5x = 15 – 8 + 5
-2x = 12
x = -6
Therefore the value of x is -6.
Problem 6 :
4t - 3 - (3t + 1) = 5t - 4
Solution :
4t - 3 - (3t + 1) = 5t - 4
4t - 3 - 3t -1 = 5t - 4
By combining the like terms.
4t - 3t – 5t = -4 + 3
-4t = -1
t = 1/4
Therefore the value of t is 1/4.
Problem 7 :
5(x - 1) - 2(x + 8) = 0
Solution :
5(x - 1) - 2(x + 8) = 0
5x - 5 - 2x - 8 = 0
By combining the like terms.
5x - 2x - 5 - 8 = 0
3x - 13 = 0
10x = 0
x = 0
Therefore, the value of x is 0.
Problem 8 :
1 - (x - 2) - [(x - 3) - (x - 1)] = 0
Solution :
1 - (x - 2) - [(x - 3) - (x - 1)] = 0
1 - x + 2 - [x - 3 - x + 1] = 0
1 - x + 2 - x + 3 + x - 1 = 0
By combining the like terms.
1 + 2 + 3 -1 - x - x + x = 0
5 - x = 0
5 = x
Therefore, the value of x is 5.
Problem 9 :
4(3p + 2) – 5(6p - 1) = 2(p - 8) – 6(7p - 4)
Solution :
4(3p + 2) – 5(6p - 1) = 2(p - 8) – 6(7p - 4)
By using distributive property.
12p + 8 – 30p + 5 = 2p - 16 – 42p + 24
By combining the like terms.
12p – 30p + 5 + 8 = 2p – 42p + 24 – 16
-18p + 13 = -40p + 8
Add 40p on both sides.
-18p+40p+13 = 8
Subtract 13 on both sides.
22p = 8-13
22p = -5
Divide by 22 on both sides.
p = -5/22
Problem 10 :
3(5x - 7) + 2(9x - 11) = 4(8x - 7) – 111
Solution :
3(5x - 7) + 2(9x - 11) = 4(8x - 7) – 111
By using distributive property.
15x – 21 + 18x – 22 = 32x – 28x - 111
By combining the like terms.
15x + 18x – 21 – 22 = 32x – 28x - 111
33x – 43 = 4x – 111
Subtract 4x on both sides.
33x – 43 – 4x = – 111
Add 43 on both sides.
29x = 43 - 111
29x = -68
Divide by 29 on both sides.
x = -68/29
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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