## Hard Algebraic Equations

**Conquer GCSE/IGCSE/GCE(OL) Linear Algebra Equations with Ease!**
Linear algebra equations might seem like a daunting hurdle on your GCSE/IGCSE/GCE(OL) math journey, but fear not! This comprehensive tutorial is here to equip you with the knowledge and skills to tackle even the most challenging problems. We'll break down complex concepts into clear, step-by-step explanations, making linear equations a breeze.

By the end of this tutorial, you'll be able to:

- Identify different types of linear equations.
- How to solve by factorization
- Apply effective strategies to solve for variables.
- Grasp the relationship between linear equations and graphs.
- Approach more complex linear algebra problems with confidence.

So, whether you're a GCSE, IGCSE, or GCE(OL) student looking to solidify your foundation or someone aiming to ace your exams, this tutorial is your perfect companion. Let's dive in and conquer those linear equations!

#### Solving equations

An equation is almost a sort of seesaw: you add something to the left, lose the balance and are forced to do the same to the right; you divide and multiply by something, once again,
the same must be done to the other side; if you subtract something, there is no exception. Therefore, solving equation means, getting rid of everything around *x* by *seesaw* method.

**E.g.1**

2(x + 5) = 18

:- 2 => 2(x + 5) :- 2 = 18 :- 2

x + 5 = 9

- 5 => x + 5 - 5 = 9 - 5

x = 4

**E.g.2**

5(x - 2) = 2(x - 3)

5x - 10 = 2x - 6

+10 => 5x - 10 + 10 = 2x - 6 + 10

5x = 2x + 4

-2x => 5x - 2x = 2x - 2x + 4

3x = 4

:-3 => 3x / 3 = 4 /3

x = 1.3

**E.g.3**

4(x + 4) + 3(x -3) = 2(x -3) + 12

4x + 16 + 3x - 9 = 2x - 6 + 12

7x + 7 = 2x + 6

- 7 => 7x + 7 - 7 = 2x + 6 - 7

7x = 2x - 1

-2x => 7x - 2x = 2x - 2x -1

5x = -1

:-5 => 5x / 5 = -1 / 5

x = -0.2

**E.g.4**

(x + 5) / 4 = (x -3) / 2

X 4 => 4 X (x + 5) /4 = 4 X (x- 3) / 2

(x + 5) = 2 (x -3)

x + 5 = 2x - 6

- 5 => x +5 -5 = 2x - 6 - 5

x = 2x - 11

-2x => x - 2x = 2x - 2x -11

-x = -11

-1 X x = 11

**E.g.5**

3 + 2(x + 5) = 3 - (2x - 1)

3 + 2x + 10 = 3 -2x + 1

13 + 2x = 4 - 2x

-13 => 2x + 13 - 13 = 4 - 2x - 13

2x = -2x - 9

+2x => 2x + 2x = 2x - 2x - 9

4x = -9

:- 4 => 4x / 4 = -9 / 4

x = -2.25

**Practice is the key to mastering maths; please visit this page, for more worksheets.**

#### Hard Equation Generator

With this simple programme, you can generate questions at random, along with answers - unlimited number of questions. Generate the question first, work out the solution and then check with the answer shown below the question.