Question

An equation and the steps to solve it are shown below:

7x − one over two (8x + 4) = 6

Step 1: 7x − 4x − 2 = 6
Step 2: 3x − 2 = 6
Step 3: 3x − 2 + 2 = 6
Step 4: 3x = 6
Step 5: x = 2

Which step was the error made and why?

Step 1, because incorrect signs have been used

Step 2, because the terms have been added incorrectly

Step 3, because a number has been added only to one side of the equation

No error was made

Answer 1

step 3....because a number has been added only to one side of the equation

Answer 2

Step 3, because a number has been added only to one side of the equation

Explanation:

Here, the given equation is,

`7x-(1)/(2)(8x+4)=6`

The steps for solving this equation would be,

Step 1 : Apply distributive property on left side of the equation,

`7x-4x-2=6`

Step 2 : Combine like terms in left side,

`3x-2=6`

Step 3 : Add 2 on both sides ( additive property of equality ),

`3x-2+2 = 6+2`

Step 4 : Combine like terms,

`3x=8`

Step 5 : Isolate x,

`x=(8)/(3)`

Thus, by the above explanation it is clear that he did it mistake on step 3, ( he did not add 2 on right side of the equation ),

Hence, Third option is correct.