Removing signs of grouping:

Linear equations in one variable of Class 8

If signs of grouping appear in an equation they should be removed in the manner indicated in chapter 9 of this course. For example, solve the equation. 

5 = 24 - [x-12(x-2) - 6(x-2)]

Notice that the same expression, x-2, occurs in both parentheses. By combining the terms containing (x-2), the equation becomes

5 = 24 - [x-18(x-2)]

Next, remove the parentheses and then the bracket, obtaining

5 = 24 – [x – 18x + 36]

= 24 – [36 – 17x]

= 24 – 36 + 17x

= –12 + 17x

Subtracting 17x from both members and then subtracting 5 from both members, we have

–17x = –12 – 5

–17x = –17

Divide both members by -17. The solution is

x=1

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