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Equations Level 5Practise solving simple linear equations with this multi-level online exercise. |
This is level 5: more complex equations requiring multiple steps to find the solution. You will be awarded a trophy if you get at least 9 correct and you do this activity online.
InstructionsTry your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file. |
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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the i asp?ID_Top 'Starter of the Day' page by Ros, Belize: "A really awesome website! Teachers and students are learning in such a fun way! Keep it up..." Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry: "Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils. |
Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month. The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing. Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page. |
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Featured ActivityStriped Sweets Colour the sweet wrappers so that no two are the same. A multi-level activity designed to encourage a systematic strategy for finding all of the different permutations. |
AnswersThere are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer. A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves. Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members. If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now: Subscribe |
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Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic. | ||
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If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows: |
Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes. |
It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org. When planning to use technology in your lesson always have a plan B! |
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Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments. |
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Scan the QR code below to visit the online version of this activity.
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Level 1 - Simple equations where the solution can be found by performing one operation on both sides of the equation.
Example: \(8n = 64\)
Level 2 - Simple equations where the solution can be found in two steps.
Example: \(9e + 6 = 78\)
Level 3 - Equations where a multiple of the unknown and a constant are on both sides.
Example: \(4y - 7 = 3y - 4\)
Level 4 - Equations including brackets.
Example: \(2(4r + 7) - 9 = 21\)
Level 5 - More complex equations requiring multiple steps to find the solution.
Example: \(6(10h + 3) + 4 = 7h + 287\)
Solve to find Fractions - A four-level set of exercises in which all of the equations have solutions that are fractions.
Example: \( 5x+2=2x+4\)
Equations with Fractions - A five-level set of exercises taking your equation solving skills one step further.
Example: \( \frac{6x-4}{2}=13 \)
Old Equations - Solve these linear equations that appeared in a book called A Graduated Series of Exercises in Elementary Algebra by Rev George Farncomb Wright published in 1857.
Nevertheless - A two-player, equation-making game based on Level 2 type equations.
Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.
More on this topic including lesson Starters, visual aids and investigations.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
See the National Curriculum page for links to related online activities and resources.
Here is an example showing a good way to solve an equation of this type (Level 5) by thinking of the two sides of the equation as two sides of a balance. The equation will remain balanced only if you do the same thing (multiply, divide add or subtract) to both sides.
3(3x - 2) + 8 = 4x + 3
First multiply out (expand) the brackets
9x - 6 + 8 = 4x + 3
Collect together like terms
9x + 2 = 4x + 3
Subtract 2 from both sides
9x = 4x + 1
Subtract 4x from both sides
5x = 1
Divide both sides by 5
x = 0.2
Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
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Henry J. Spencer, The Gryphon School, Sherborne
Thursday, May 25, 2017
"I am commenting to show you a wrong answer. Me, my teacher and my friends around me have been trying to solve this equation. We believe that you have your answer wrong and you may need to check it. The question is:
2(4y-3)=5(y+6)
If you worked out the answer you would know that y=12. Unfortunately, when I submitted that answer, it was wrong. I hope you take this into consideration and I hope I will not find any more problems that I believe are wrong.
Your sincerely,
Henry J. Spencer."
Transum,
Friday, May 26, 2017
"Thanks Henry for pointing out the error with Level 5 question 2. It has now been corrected. The questions that you see are drawn from a database containing a number of different versions of the question type. One of the versions is chosen each time the page is loaded. I hope you will not find any other errors but please let me know if you do. I am very grateful for the time you took to flag up the mistake. Thank you again."
Ibby Gaze, Twitter
Wednesday, November 15, 2017
Martin Ward, Spain
Monday, January 15, 2024
"This resource is absolutely incredible. So useful. Just enough questions. Just enough challenge. Gives the students control about which level they would like to attempt. And it self-assesses, too!"