Help with simple math question?

Question

18 = 3|4x - 10|

Answer 1

so 6 = |4x - 10|

so 4x = |16| or 4x = |-4|

so x = 4 or x = 1

i am unsure whether most answers correctly understand the concept of absolute values...

Answer 2

It's the absolute value that makes this one a little tricky. First, we have to consider the two possible cases:

18 = 3(4x - 10) if 4x - 10 >= 0

and

18 = 3(10 - 4x) if 4x - 10 < 0

That's the definition of absolute value. So, we just need to solve each of the cases.

First case:
18 = 3(4x - 10) ==>
18 = 12x - 30 ==>
12x = 48 ==>
x = 4
And since 4(4) - 10 = 6 >= 0, this is a valid solution.

Second case:
18 = 3(10 - 4x) ==>
18 = 30 - 12x ==>
12x = 12 ==>
x = 1
Since 4(1) - 10 = -6 < 0, this is also a valid solution.

So, the solutions are x = 4 and x = 1.

Answer 3

Okay, your answer is: x=1 or x=4. There are two answers, and here's how (it all has to do with those absolute brackets)...

When solving for a variable that's inside absolute brackets, you have to solve with the "answer" (the number on the other side of the equal sign) as it is AND as if it was multiplied by -1. However, before you do this you have to get rid of anything outside of the absolute brackets (in this case the 3). When whatever outside the absolute brackets is being added or subtracted you NEED to do this WITHOUT touching anything inside the absolute brackets, however with multiplication or division you can just do the application using distributive property. I'll show you how to solve the problem using both ways.

Now the work:

18 = 3|4x - 10|
18/3 = [3|4x - 10|]/3
6 = 4x - 10
(Now this where the you spit the problem into two separtate problems with two separtate answers.)
6 = 4x - 10
6 + 10 = 4x - 10 + 10
16 = 4x
16/4 = 4x/4
x = 4

-6 = 4x - 10
-6 + 10 = 4x - 10 + 10
4 = 4x
4/4 = 4x/4
x = 1

Now, check your answers because sometimes only one answer works or neither. Just put 4 in as x and then 1 in as x (in this case both answers work). Just make sure you remember that |-6| = 6.

Finally, the alternative method (this is the version I use, even though must people use the above):

18 = 3|4x - 10|
18 = 12x - 30

18 = 12x - 30
18 + 30 = 12x - 30 + 30
48 = 12x
48/12 = 12x/12
x = 4

-18 = 12x - 30
-18 + 30 = 12x - 30 + 30
12 = 12x
12/12 = 12x/12
x = 1

Answer 4

x = 4 or x = 1

Answer 5

x=4 and 1

Answer 6

18=3 x 6

so the the positive of absolute of 4x-10=6

or -6 depending on how you look at it...so

4x=6--10 =16 which would be 4

or
4x=-6--10= -6+10=4 which would be 1

Answer 7

To make the equation easier, divide both sides by 3 first.

The result is 6 = [4x - 10]. Then, let's work on the absolute value. To solve abs value eqns, you have to solve it twice (one positive and one negative).

Thus your eqns lead to 6 = 4x - 10 and 6 = -(4x - 10).

Solve the eqns separately. To solve the first one, add 10 on both sides then divide the answer by 4. The result is x = 16/4 or 4.

To solve the second eqn. distribute the negative sign. The result is 6 = -4x + 10. Subtract 10 from both sides and divide the result by -4. The answer is x = -4/-4 or 1.

The answers then are 4 and 1.

Answer 8

18 = 3|4x - 10|
6=|4x-10| so either
6=4x-10 => x=4 or
6=10-4x => x=1

Doug

Answer 9

18 = 12x-30 Absolute value is always positive

12X = 18 +30

12X = 48 Divide both sides by 12 and

1x = 4 Check: 18=3 times 4x4-30
18 =12x4-30 18=(3x16)-10 18=48-30=18 18=18

Answer 10

x= 1 or 4 because:

18 = 3|4x - 10|
divide each side by 3
6= |4x-10|

Now there are 2 cases:
4x-10 is greater than zero
4x-10 is less than zero

If 4x-10 is greater than zero, you have
6=4x-10
Then add 10 to both sides and you get
6=4x
Then divide each side by 4
4=x

If 4x-10 is less than zero, you have
6= -(4x-10)
Then distribute the negative sign and you get
6= -4x+10
Then subtract 10 from both sides and you get
-4 = -4x
Then divide each side by negative 4 and you get
1=x

When you are done, substitute the answer in to check.

So x= 1 or 4

Answer 11

18 = 3|4x - 10|
6 = 4x + 10
4x = - 4
x = - 1