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Resources to Help You Solve Math Equations

Whether you love math or suffer through every single problem, there are plenty of resources to help you solve math equations. Skip the tutor and log on to load these awesome websites for a fantastic free equation solver or simply to find answers for solving equations on the Internet.

Stand By for Automatic Math Solutions at Quick Math

The Quick Math website offers easy answers for solving equations along with a simple format that makes math a breeze. Load the website to browse tutorials, set up a polynomial equation solver, or to factor or expand fractions. From algebra to calculus and graphs, Quick Math provides not just the answers to your tough math problems but a step-by-step problem-solving calculator. Use the input bar to enter your equation, and click on the “simplify” button to explore the problem and its solution. Choose some sample problems to practice your math skills, or move to another tab for a variety of math input options. Quick Math makes it easy to learn how to solve this equation even when you’re completely confused.

Modern Math Answers Come From Mathway

Mathway offers a free equation solver that sifts through your toughest math problems — and makes math easy. Simply enter your math problem into the Mathway calculator, and choose what you’d like the math management program to do with the problem. Pick from math solutions that include graphing, simplifying, finding a slope or solving for a y-intercept by scrolling through the Mathway drop-down menu. Use the answers for solving equations to explore different types of solutions, or set the calculator to offer the best solution for your particular math puzzle. Mathway offers the option to create an account, to sign in or sign up for additional features or to simply stick with the free equation solver.

Wyzant —​ Why Not?

Wyzant offers a variety of answers when it comes to “how to solve this equation” questions. Sign up to find a tutor trained to offer online sessions that increase your math understanding, or jump in with the calculator that helps you simplify math equations. A quick-start guide makes it easy to understand exactly how to use the Wyzant math solutions pages, while additional resources provide algebra worksheets, a polynomial equation solver, math-related blogs to promote better math skills and lesson recording. Truly filled with math solutions, Wyzant provides more than just an equation calculator and actually connects you with people who are trained to teach the math you need. Prices for tutoring vary greatly, but access to the website and its worksheets is free.

Take in Some WebMath

Log onto the WebMath website, and browse through the tabs that include Math for Everyone, Trig and Calculus, General Math and even K-8 Math. A simple drop-down box helps you to determine what type of math help you need, and then you easily add your problem to the free equation solver. WebMath provides plenty of options for homeschoolers with lesson plans, virtual labs and family activities.

Khan Academy Offers More Than Answers

A free equation solver is just the beginning when it comes to awesome math resources at Khan Academy. Free to use and filled with videos that offer an online teaching experience, Khan Academy helps you to simplify math equations, shows you how to solve equations and provides full math lessons from Kindergarten to SAT test preparation. Watch the video for each math problem, explore the sample problems, and increase your math skills right at home with Khan Academy’s easy-to-follow video learning experience. Once you’ve completed your math video, move onto practice problems that help to increase your confidence in your math skills.


solving equations questions hard


Hard algebraic 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.

2(x + 5) = 18 :- 2 => 2(x + 5) :- 2 = 18 :- 2 x + 5 = 9 - 5 => x + 5 - 5 = 9 - 5 x = 4

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

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

(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

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.

Recommended Reading

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Maths is challenging; so is finding the right book. K A Stroud, in this book, cleverly managed to make all the major topics crystal clear with plenty of examples; popularity of the book speak for itself - 7 th edition in print.

Recommended - GCSE & iGCSE

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This is the best book available for the new GCSE(9-1) specification and iGCSE: there are plenty of worked examples; a really good collection of problems for practising; every single topic is adequately covered; the topics are organized in a logical order.

Recommended for A Level

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This is the best book that can be recommended for the new A Level - Edexcel board: it covers every single topic in detail;lots of worked examples; ample problems for practising; beautifully and clearly presented.

One to one maths interventions built for KS4 success

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GCSE Maths

Solving Equations

Here we break down everything you need to know about solving equations. You’ll learn what linear and quadratic algebraic equations are, and how to solve all the different types of them.

At the end you’ll find solving equations worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is an equation?

An equation is a mathematical expression that contains an equals sign .

There are two sides to an equation, with the left side being equal to the right side.

Equations will often involve algebra and contain unknowns (variables) which we often represent with letters such as x or y .

We can solve simple equations and more complicated equations to work out the value of these unknowns; they could involve fractions, decimals or integers.

Step-by-step guide: Forming and solving equations

What is an equation?

Solving equations worksheets

Get your free solving equations worksheet of 20+ questions and answers. Includes reasoning and applied questions.

How to solve equations

In order to solve equations, we need to work out the value of the unknown variable by adding, subtracting, multiplying or dividing both sides of the equation by the same value.

In GCSE Maths there are two main types of equations that we need to solve, both of which are covered below.

Explain how to solve equations

Explain how to solve equations

Solving equations methods

Within solving equations, you will find lessons on linear equations and quadratic equations.

Each method of solving equations is summarised below. For detailed examples, practice questions and worksheets on each one follow the links to the step by step guides.

1. Linear equations

There are 5 main types of linear equations we can solve.

Example of solving an equation with:

  • One unknown

2 Unknown on both sides

3 With brackets

4 With fractions

Step-by-step guide: Equations with fractions

5 Powers (exponents) and roots

We can check that our solution is correct by substituting it into the original equation.

Step-by-step guide: Linear equations

Step-by-step guide: Iteration maths

2. Quadratic equations

There are 4 main ways to solve quadratic equations.

Example of solving a quadratic equation by:

  • Factorising

Step-by-step guide: Solving quadratic equations by factorising

2 Quadratic Formula

Step-by-step guide: Quadratic formula

3 Complete the square

Step-by-step guide: Completing the square

4 Graphically

Solving equations graphically

The solutions/roots are found when the graph equals 0 (crosses the x -axis).

Step-by-step guide: Solving quadratic equations graphically

See also: Quadratic equations

Practice solving equations questions

1. Solve: 4x-2=14

GCSE Quiz False

Add 2 to both sides

Divide both sides by   4

2. Solve: 3x-8=x+6

Add 8 to both sides

Subtract x from both sides

Divide both sides by 2

3. Solve: 3(x+3)=2(x-2)

Expanding the brackets

Subtract 9 from both sides

Subtract 2x from both sides

4. Solve: \frac{2 x+2}{3}=\frac{x-3}{2}

Multiply by 6 (the lowest common denominator) and simplify

Expand the brackets

Subtract 4 from both sides

Subtract 3x from both sides

5. Solve: \frac{3 x^{2}}{2}=24

Multiply both sides by 2

Divide both sides by 3

Square root both sides

6. Solve by factorising: x^{2}-13 x+30=0

Factorise as a double bracket

Set each bracket equal to zero and solve, hence

x=3 or x=10

7. Solve by factorising: 2 x^{2}+3 x-20=0

8. (H) Solve by using the quadratic formula:  x^{2}-4 x-3=0 give your answer to 3 significant figures

Substitution into the quadratic formula gives

x=\frac{-(-4)+\sqrt{(-4)^{2}-4(1)(-3)}}{2(1)} \quad \quad \quad \; x=\frac{-(-4)-\sqrt{(-4)^{2}-4(1)(-3)}}{2(1)} \\ x=2+\sqrt{7} \quad \quad \quad \quad \quad \quad \quad \quad x=2-\sqrt{7} \\ x=4.65 \; (3.5 . f) \quad \quad \quad\quad \quad \quad x=-0.646 \; (3.s.f)

9. (H) Solve by using the quadratic formula:  2 x^{2}+4 x-4=0 give your answer to 3 significant figures

x=\frac{-(4)+\sqrt{(4)^{2}-4(2)(-4)}}{2(2)} \quad \quad \quad \; x=\frac{-(4)+\sqrt{(4)^{2}-4(2)(-4)}}{2(2)} \\ x=-1+\sqrt{3} \quad \quad \quad \quad \quad \quad \quad \quad x=-1-\sqrt{3} \\ x=0.732 \; (3.s.f) \quad \quad \quad \quad \quad \quad x=-2.73 \; (3.s.f)

10. (H) Solve by completing the square: x^{2}-6 x+5=0

Completing the square

Add 4 to both sides

Add 3 to both sides

So x=5, \; x=1

Solving equations GCSE questions

1. Solve: 4y = 36

2. Solve: x 2 − 5x − 24 = 0

x = − 3, x = 8

3. Solve: 7y − 8 = 13

Learning checklist

  • Use algebraic methods to solve linear equations
  • Solve quadratic equations algebraically by factorising
  • Solve quadratic equations algebraically by completing the square (H)
  • Solve quadratic equations algebraically by using the quadratic formula (H)
  • Solve quadratic equations by finding approximate solutions using a graph

The next lessons are

  • Quadratic equations
  • Simultaneous equations
  • Rearranging equations

Still stuck?

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  1. Solving Equations: Hard

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