Equations Level 4

Practise solving simple linear equations with this multi-level online exercise.

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This is level 4: equations including brackets. You will be awarded a trophy if you get at least 9 correct and you do this activity online.

 $$4(7j + 3) - 7 = 117$$ $$j=$$ $$9(2r + 4) - 1 = 107$$ $$r=$$ $$6(9a - 7) + 9 = 507$$ $$a=$$ $$7(5x - 3) + 8 = 127$$ $$x=$$ $$478 = 8(7t + 3) + 6$$ $$t=$$ $$5(6y + 1) + 8 = 283$$ $$y=$$ $$812 = 10(10u - 8) - 8$$ $$u=$$ $$6(5z - 9) + 5 = 101$$ $$z=$$ $$4(8m + 3) + 9 = 19221$$ $$m=$$ $$6(3t - 8) + 2 = 35$$ $$t=$$ $$9(4s + 1) - 6 = 147$$ $$s=$$ $$8(6a + 1) + 10 = 114$$ $$a=$$
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This is Equations level 4. You can also try:
Level 1 Level 2 Level 3 Level 5 Level 6

Instructions

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.

Transum.org

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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Pentransum

Answer multiple choice questions about basic mathematical ideas. If you get a number of questions correct you will be invited to post a question of your own. The bank of questions grows larger every day.

Answers

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.

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Teachers

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:

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

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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© Transum Mathematics :: This activity can be found online at:
www.transum.org/software/SW/Starter_of_the_day/students/Equations.asp?Level=4

Description of Levels

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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.

Example: $$\frac{10e+2}{5}=2$$

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.

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.

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Example

Here is an example showing a good way to solve an equation of this type (Level 4) 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.

2(3x - 4) + 1 = 5
Subtract 1 from both sides
2(3x - 4) = 4
Divide both sides by 2
3x - 4 = 2
Add 4 to both sides
3x = 6
Divide both sides by 3
x = 2

Another method:

2(3x - 4) + 1 = 5
First multiply out (expand) the brackets
6x - 8 + 1 = 5
Collect together like terms
6x - 7 = 5
Add 7 to both sides
6x = 12
Divide both sides by 6
x = 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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