Equations Level 6
Practise solving simple linear equations with this multi-level online exercise.
This is level 6: equations involving algebraic fractions. You will be awarded a trophy if you get at least 15 correct and you do this activity online.
Try 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.
This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.
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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 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:
"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"
Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:
"Very good starters, help pupils settle very well in maths classroom."
There 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.
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Learning 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.
Are 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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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: \(6(10h + 3) + 4 = 7h + 287\)
Level 6 - Equations involving algebraic fractions.
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.
More on this topic including lesson Starters, visual aids and investigations.
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 6) 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.
Multiply both sides by the LCM of 3 and 5 which is 15.$$5(x-3)=3(x+3)$$ $$5x-15=3x+9$$
Add 15 to both sides$$5x=3x+24$$
Subtract 3x from both sides$$2x=24$$ $$x=12$$
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.