## 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 |
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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 |
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4 |

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

2x – 5 – (1 – x) |
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4 |

3x – 6 |
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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 **

2x^{2} + 3x |
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7x |

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

2x + 3 |
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7 |

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

2x + 3 |
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7 |

7• | 2x + 3 |
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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 |
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4 |

3(5x + 6) |
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3•4 |

15x + 18 – 8x + 32 |
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12 |

7x + 50 = 89

7x = 39

x = | 39 | |

7 |

The right answer is "A" option.

**Solution – 8 **

1. 5x + 5 – 2x + x^{2} = 3 – x + x^{2} – 10

2. y + 3 – 2y – y^{2} = 8y + 12 – y^{2}

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

5x + 5 – 2x + x^{2} = 3 – x + x^{2} – 10

5x – 2x + x^{2} – x^{2} + x = 3 – 10 – 5

4x = - 12

x = - 3

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

y – 2y – y^{2} – 8y + y^{2} = 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.

RISE KNOWLEDGE

20/06/2018

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