THE SOLUTIONS OF EQUATIONS TEST - I

Mathematics lesson, first degree equation questions. Solutions of questions about first degree equations. Step by step solutions of the equation questions.



Solution – 1 


2x – 5 
- 7 
- 9 = 1 - x - 2
4
2
4





We take the terms that contains unknown x value to left side of equality, other terms to right side of the equation.

2x – 5 
1 – x
= 7 – 2 + 9
2
4
4




Let we do addition and subtraction operations at the both sides of the equality.


2x – 5 – (1 – x) 
= 7 + 7
2
4





3x – 6 
= 21
2
4




The denominators which at the both sides of equality can be simplified.

3x – 6 = 21
2




3x – 6 = 42

3x = 48

x = 16


The right answer is "A" option.


Solution – 2 

2x + 1 + 18 = 2√2x + 1 + 11

Let we addition the terms that have an unknown x value at left side of the equality, and let we addition the other terms at right side of equality.

18 - 11 = 2√2x + 1 - √2x + 1

7 = √2x + 1 (2 – 1)

7 = √2x + 1

Now, we are taking square of both sides of equality.

49 = 2x + 1

2x = 48

x = 24


The right answer is "C" option.


Solution– 3 

1. 3x + 12 – 5x = x – 3  + 1
2




2. 2y + 1 – y = 2 + 3y – 9
3




We find x value by the solution of the first equation.

3x – 5x – x – 3 = 1 – 12
2




-2x – x – 3 = - 11
2




3 – x – 2x = - 11
2




3 – x – 4x = - 11
2




3 – 5x = -22

-5x = - 25

x = - 25
- 5




x = 5


We find y value by the solution of the second equation.

2y + 1 – y  = 2 + 3y – 9
3




2y – y – 3y = 2 – 9 – 1
3



y – y = - 8
3



 

4y = - 8
3




-4y = -24

y - 24
- 4




y = 6

x + y = 5 + 6

= 11


The right answer is "E" option.


Solution– 4 

1. 3x – 9 + 2x – 5 = 6x – 11 + 2

2. 8 – 3y + 1 = 5 – 2y + 6


We find x value by the solution of the first equation.

3x – 9 + 2x – 5 = 6x – 11 + 2

The terms that have unknown x value are collected to a side, the other terms collected at other side.

3x + 2x – 6x = -11 + 2 + 5 + 9

-x = 5

x = - 5


We find y value by the solution of the second question.


8 – 3y + 1 = 5 – 2y + 6

-3y + 2y = 5 + 6 – 8 – 1

-y = 2

y = - 2

x + y = - 5 – 2 

= - 7


The right answer is "B" option.


Solution – 5 

1. (3 – 2x)2 = (x + 1)2

2. √z + 2 + 10 = 12 – 3√z + 2 


Let we solution the first equation.


(3 – 2x)2 = (x + 1)2

Let we simplify the exponents of the both sides.

3 – 2x = x + 1

3x = 2

x =2
3




The solution of the second equation.

z + 2 + 10 = 18 – 3√z + 2

We are addition the rooted terms at the left side of equality, other terms at right side of the equality.

z + 2 + 3√z + 2 = 18 – 10 

4√z + 2  = 8

If we divide 4 the both sides of the equality.

z + 2 = 2

Now, we takes the square of the both sides of the equality.

z + 2 = 4

z = 2

x + z = 2 + 2
3




= 8
2




The right answer is "D" option.


Solution – 6 

2x2 + 3x 
= x + 9
14
7x




Let we divide by x the numerator and denominator of the fraction that at left side of the equality.


2x + 3 
= x + 9
14
7




Let we multiplication by 7 the both sides of the equality.


2x + 3 
= x + 9
2.7
7




7•2x + 3 
=x + 9•7
2•7
7




2x + 3 = x + 9
2




Let we multiplication by 2 the both sides of the equality.

2•(2x + 3) = 2• x + 9
2





4x + 6 = x + 9

3x = 3

x = 1

The right answer is "C" option.


Solution – 7 

Equationtest1S2


Let we addition the terms that have an unknown x variable on the left side of the equality, and let we addition the other terms on the right side of the equality.

5x + 6 
2x – 8 
= 11 
+15
4
3
3
4





3(5x + 6) 
– 4(2x – 8) 
= 4.11 
+ 3.15
3•4
3•4
3•4
3•4





15x + 18 – 8x + 32 
= 89
12
12





7x + 50 = 89

7x = 39

x =39
7




The right answer is "A" option.


Solution – 8 

1. 5x + 5 – 2x + x2 = 3 – x + x2 – 10 

2. y + 3 – 2y – y2 = 8y + 12 – y2


We find "x" value by solution of the first equation.


5x + 5 – 2x + x2 = 3 – x + x2 – 10

5x – 2x + x2 – x2 + x = 3 – 10 – 5 

4x = - 12

x = - 3


We find "y" value by solution of the second equation.

y – 2y – y2 – 8y + y2 = 12 – 3 

-9y = 9

y = - 9/9

y = -1


x.y = (-3) • (-1)

= 3

The right answer is "E" option.


Solution– 9 

1. 3a + 8 – a = 2 – a + 11

2. 11b – 35 + 2b = 37 + 5b 

The solution of the first equation.

3a + 8 – a = 2 – a + 11

3a – a + a = 2 + 11 – 8 

3a = 5

a = 5
3




The solution of the second equation.

11b + 2b – 5b = 37 + 35

8b = 72

b = 9

a.b = 5•9
3



= 15


The right answer is "C" option.


Solution – 10 

10t + 3 – 7t = 163 – 17t 


10t – 7t + 17t = 163 – 3 

20t = 160

t = 8

The right answer is "C" option.


Questions Of This Test

First Degree Equation Subject



RISE KNOWLEDGE

20/06/2018

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