Question

3.

Circle the step where the error has occurred. Explain why it is an error.
Given
Step 1: Distribute
Step 2: Combine like Terms
Step 3: Subtraction Property of Equality
Step 4: Addition Property of Equality
Step 5: Division Property of Equality
2(10 - 13x) + 9x = -34x + 60
20- 26x + 9x = -34x + 60
20 - 17x = -34x + 60
-17x = -34x + 40
-51x = 40
x = -51/40
I don't understand this question ​

Answer 1

The step 4 and step 5 both are wrong.

Explanation:

Consider the provided steps:

Given:
`2(10-13x)+9x=-34x+60`

Step 1: Distribute

`20-26x+9x=-34x+60`

Step 2: Combine like terms

`20-17x=-34x+60`

Step 3: Subtraction property of equality

`20-20-17x=-34x+60-20`

`-17x=-34x+40`

Step 4: Addition property of equality

`-17x+34x=-34x+34x+40`

`17x=40`

Step 5: Division property

`x=(40)/(17)`

From the above calculation we can concluded that the step 4 and step 5 both are wrong.

Step 4 should be
`17x=40`

Step 5 should be
`x=(40)/(17)`

Answer 2

Step 3.

Operation error, where the sign on the number changes from -ve to +ve where shifted to the left side of the equation.

Explanation:

Given that 2(10 - 13x) + 9x = -34x + 60

Step 1. Distribute

20-26x+9x=-34x+60

Step 2: Combine like Terms

20-17x=-34x+60 -------------------------(-26x+9x = -17x)

Step 3: subtraction property of equality

-17x+34x=60-20--------------------- (60-20 =40)

-17x+34x=40

Step 4 :Addition property of Equality

-17x+34x=40-------------------(-17x+34x =17x)

17x=40

Step 5: Division property of Equality

17x=40

17x/17 = 40/17

x=40/17

Answer

x=40/17

Errors

In step 3

-17x+34x = 17 x and not 51x

In step 5

-51x=40

x=-40/51 (not the other way round, -51/40) however correct operation is supposed to be;

17x=40, hence x =40/17