Can someone answer this math problem..and explain please??

Question

½ | 2x+1 |=3x

Im confused because there is a variable on both sides and I'm not sure how to move it with the absolute value

Answer 1

get rid of the half by * both sides by 2

|2x + 1| = 6x

now, if we consider the absolute valu of say |x| = 2, x could have been -2 or 2. Set the problem up the same way.

2x + 1 = 6x or 2x + 1 = - 6x

1 = 4x or 1 = -8x

x = 1/4 or x = -1/8

Answer 2

1/2 ∣2x + 1∣= 3x

Clear the fraction

2(1/2)∣2x + 1∣= 2(3x)

1∣2x + 1∣= 6x

Remove the absolute value bars and insert parenthesis

1(2x + 1) = 6x

The distributive property

2x + 1 = 6x

Transpose 2x

2x + 1 - 2x = 6x - 2x

1 = 4x

Divide both sides of the equation by 4

1/4 = 4x /4

1/4 = x

- - - - - - - - -

Check

1/2∣2x + 1∣ = 3x

Remopve absolute value bars and insert parenthesis

1/2(2x + 1) = 3x

INsert the x = 1/4

1/2[2(1/4) + 1)] = 3(1/4)

1/2(2/4 + 1) = 3/4

1/2 ( 2/3 + 4/4) = 3/4

Add inside the parentheisi

1/2(6/4) = 3/4

Multiply the right side of the equation

6/8 = 3/4

simplify the right side of the equation

3/4 = 3/4

- - - - - - -s-

Answer 3

½ | 2x+1 |=3x

Multiply both sides by 2:
|2x + 1| = 6x

When an absolute value expression (AVE) (|2x + 1|) is set equal to a second expression (6x), make two equations, one where the inside of the AVE is equal to the 2nd:
2x + 1 = 6x

and one where the inside of the AVE is equal to the opposite of the 2nd:
2x + 1 = - 6x

Solve both for x
2x + 1 = 6x 2x + 1 = -6x
1 = 4x 1 = -8x
x = 1/4 x = -1/8

Two answers, but both must be checked against the original equation:
½ | 2(1/4)+1 | = 3(1/4)
½ | 1/2+1 | = 3/4
½ | 3/2 | = 3/4
½ (3/2) = 3/4
3/4 = 3/4 <== checks

½ | 2(-1/8)+1 | = 3(-1/8)
½ | -1/4+1 | = -3/8
½ | 3/4 | = -3/8
½ (3/4) = -3/8
3/8 = -3/8 <== does *not* check

So, the only answer is x = 1/4 or 0.25

Answer 4

In many mathematical problems there is one and only one answer. In other problems (like this one) there are more than one possible answer. You are correct to assume that you must treat the absolute value symbols differently than you would parenthesis in solving this problem.

One method is to create two different problems without the use of absolute value symbols for the two conditions where the formula inside the absolute value symbols is positive and one for when the formula is negative.
½ ( 2x+1 )=3x
½ (-2x-1 )=3x
The standard algebra techniques you have been taught will then apply and you can find potentially two different answers or in some cases the two answers will be the same.
½ ( 2x+1 )=3x
x+½=3x
½=2x
x=1/4


½ (-2x-1 )=3x
-x-½ =3x
-½ =4x
x=-1/8

Answer 5

1/2(2x + 1) = 3x
Finding the value of x:
x + 1/2 = 3x
1/2 = 2x
x = 1/4

Proof:
1/2(2[1/4] + 1) = 3(1/4)
1/2(1/2 + 1) = 3/4
1/4 + 1/2 = 3/4
3/4 = 3/4

Answer 6

1/2l2x+1l=3x-------------*2
l2x+1l=6x
2x+1=6x (x>or=-1/2) or2x+1=-6x (x<-1/2)
4x=1 -8x=1
x=1/4 x=-1/8 refused
so x=1/4 only

Answer 7

½ | 2x+1 |=3x
=>| 2x+1 |= 2* 3x
=>| 2x+1 |= 6x
=>2x+1= ±6x
=>2x+1=6x OR =>2x+1= -6x
=>-4x=-1 ...OR => 8x = -1
=> x=1/4 ....OR => x = -1/8


OR SQUARE BOTH SIDES

½ | 2x+1 |=3x
=>1/4(4x^2 + 4x + 1)=9x^2
=> 4x^2 + 4x + 1 = 36x^2
=> 32x^2 - 4x - 1 = 0
=> (8x+1)(4x-1)=0
=> x=-1/8 OR x = 1/4



QED