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|3w + 4| = 6w + 1 (absolute value equations. With work to explain it please..

2 Answers

4 votes

Answer:

w = -1

Explanation:

(Possibility 1)

3w + 4 = 6w + 1

-6w -6w

------------------------

-3w + 4 = 1

-4 -4

-------------------------

-3w = -3

/-3 /-3

-------------------------

w = -1

(Possibility 2)

3w + 4 = −6w - 1

+6w +6w

-------------------------

9w + 4 = -1

-4 -4

--------------------------

9w = -5

/9 /9

--------------------------

w = -5/9

Check:

When you plug w = 1 back into the equation, IT WORKS.

When you plug w = -5/9 back into the equation, IT DOESN'T WORK.

So, w = 1 is the solution to |3w + 4| = 6w + 1

User Adam Mackler
by
3.9k points
2 votes

Answer:

w = 1

Explanation:

Because you have an absolute value that means that there are 2 possibilities, either (3x +4) is positive or negative.

Will work each case and that will give us the answers.

→ If (3x+4) is positive we have the equation

3w+ 4 = 6w +1 , subtract 3w from both sides

4 = 6w-3w+1, subtract 1 from both sides

4-1 = 6w-3w, combine like terms

3 = 3w , divide both sides by 3

1 = w

- check if our solution checks the equation given by substituting w with 1 :

|3*1+4| = 6*1+1 ;

7 = 7 is true so the one solution to the equation is w=1

→ If (3x+4) is negative we have the equation

-(3w+ 4) = 6w +1 , distribute the negative sign in parentheses

-3w -4 = 6w +1, add 3w and subtract 1 from both sides of the equation

-4 -1 = 6w +3w, combine like terms

-5 = 9w , divide both sides by 9

(-5/9) = w

- check if our solution checks the equation given by substituting w with -5/9 in the |3w + 4| = 6w + 1 :

|(3*(-5/9)+4| = 6(-5/9) +1;

|((-5/3)+(4*3/3)| = 6(-5/9) +1;

|(-5+12)/3| = (-10+3)/3;

7/3 = -7/3 not true so we reject as a solution

User Redman
by
4.4k points