# RISE KNOWLEDGE

## 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

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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