Question

Solve each of the folowing equations | x-1/2 | =3 2/3

Answer 1

4 1/6 and -3 1/3

Explanation:

To find the answer for this question, you would have to find 2 answers because of the absolute value. |x - 1/2| = 3 2/3, So, something minus one half is 3 2/3. We can find one answer by adding one half to 3 2/3 to get 3 4/6 + 3/6 and our answer is 3 7/6 or 4 1/6. One answer for the problem is 4 1/6. To find the second answer, we can do x + 1/2 is 3 2/3 because the other x is negative. The only other x value that will work is -3 1/3.

Answer 2

`\sf x = (25)/(6), -(19)/(6)\textsf{ or } x= 4(1)/(6), -3(1)/(6)`

Explanation:

`\sf [x - (1)/(2)| = 3(2)/(3)`

In order to solve the equation, we can follow these steps:

Convert an improper fraction to proper fraction:

`\sf 3(2)/(3) = (11)/(3)`

Now, rewrite the equation with the proper fraction on the right-hand side:

`\sf |x - (1)/(2)| = (3* 3+2)/(3)`

`\sf |x - (1)/(2)| = (11)/(3)`

We'll have two cases to consider, one for when the expression inside the absolute value is positive and one for when it's negative.

`\sf \textsf{Case 1: $\sf x - (1)/(2)$ is positive:}`

`\sf x - (1)/(2) = (11)/(3)`

Now, solve for x.

`\sf x = (11)/(3) + (1)/(2)`

To add these fractions, find a common denominator, which is 6:

`\sf x = (22)/(6) + (3)/(6)`

Combine t

ki. he fractions:

`\sf x = (25)/(6)`

`\sf \textsf{Case 1: $\sf x - (1)/(2)$ is negative:}`

`\sf -(x - (1)/(2)) = (11)/(3)`

First, distribute the negative sign on the left side:

`\sf -x + (1)/(2) = (11)/(3)`

Now, isolate x:

`\sf -x = (11)/(3) - (1)/(2)`

To subtract these fractions, find a common denominator, which is 6:

`\sf -x = (22)/(6) - (3)/(6)`

Combine the fractions:

`\sf -x = (19)/(6)`

Now, multiply both sides by -1 to solve for x:

`\sf x = -(19)/(6)`

So, the solutions to the equation are:

`\sf x = (25)/(6), -(19)/(6)\textsf{ or } x= 4(1)/(6), -3(1)/(6)`