2x − 1/4 (12x + 4) = 3

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

In which step was the error made and why?

A.) Step 1, because incorrect signs have been used
B.) Step 2, because the terms have been added incorrectly
C.) Step 3, because a number has been subtracted from both sides of the equation
D.) No error was made

Question

08-06-2018
Mathematics

contestada

2x − 1/4 (12x + 4) = 3

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

In which step was the error made and why?

A.) Step 1, because incorrect signs have been used
B.) Step 2, because the terms have been added incorrectly
C.) Step 3, because a number has been subtracted from both sides of the equation
D.) No error was made

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MarkV MarkV · Answer 1 · 2018-06-08T19:37:54+02:00

Hi there! The answer is A.

In which step was the error made and why? The answer was in:
A.) Step 1, because incorrect signs have been used.

In the first step the parenthesis are worked out incorrectly. When we work out the parenthesis in a function we can for instance use the rainbow method. We mustn't forget the sign that is used in front of the parenthesis.

In this particular situation the sign in front of the parenthesis is − . This means we multiply a negative (outside the parenthesis) with a positive (inside the parenthesis) and therefore end up with a negative.

When the perenthesis had been worked out correctly, we would get the following.
[tex]2x - \frac{1}{4} (12x + 4) = 3[/tex]

Rainbow method
[tex]2x - \frac{1}{4} \times 12x - \frac{1}{2} \times 4 = 3 [/tex]

Multiply
[tex]2x - 3x - 1 = 3[/tex]

Collect terms
[tex] - x - 1= 3[/tex]

Add 1 to both sides.
[tex] - x = 4[/tex]

Divide by -1.
[tex]x = - 4[/tex]

In short: the answer is A.
~ Hope this helps you!

VictorZ VictorZ · Answer 2 · 2018-06-18T10:46:27+02:00

Hi there!
The answer is [ A. ]

EXPLANATION :-

[ A. ] - Incorrect signs have been used.

We must remember th' rules of multiplication while doing calculations.
Here, th' Parenthesis are work'd out incorrectly.

Now,

Let's look at th' correct answer. If th' Parenthesis worked out Correctly :-

2x - [tex]\dfrac {1}{4}[/tex] (12x + 4) = 3

=> 2x - ([tex]\dfrac {12x}{4}[/tex] + [tex]\dfrac {4}{4}[/tex]) = 3

=> 2x - (3x + 1) = 3

=> 2x - 3x - 1 = 3

=> - x = 3 + 1

=> - x = 4

Dividin' by -1 :-

=> x = - 4

~ Hope it helps!