Answer to Question #262959 in Algebra for accoitu

Question

The activity below was given to Grade 6 learners. Answer the questions that follow:

Activity:

Write an expression using the sequence/order of operations

i. Add 5 to x, subtract the result from 1, then double what you have.

ii. Add 5 to x, double what you have, then subtract 1 from the result.

2.1.1 Two learners claim that the instructions for the two expressions are the same.

Briefly explain the important differences between the two expressions. (6)

2.1.2 Write a detailed solution for learners showing step-by-step how to do the activity.

(10)

2.1.3 Simplify each expression you found in 2.1.2 to show that they are different.

Answer 1

2.1.1) The instructions for the two expressions are not the same because from (i), you first find the result then you double it but in (ii) you subtract one from the result you get.

2.1.2) (i) take x and add 5 to get (x+5).

Subtract the above expression from one to get 1-(x+5).

Put the result in bracket and then multiply by 2 to get 2[1-(x+5)]

(ii) Take x and add 5 to get (x+5).

Double the result to get 2(x+5).

Finally subtract 1 from the result to get 2(x+5)-1

2.1.3) expression 2[1-(x+5)]=2[1-x-5]=2[-x-4]=-2x-8

The expression 2(x+5)-1=2x+10-1=2x+9

Therefore, the two expressions are different.