Question

Rewrite the equation so that none of the values have a denominator and then solve the equation.

1/3x - 5 = 5/2x - 2/3

One strategy for solving the equation above is to

a. determine the least common denominator (LCD) of all fractions in the equation,

b. then multiply the entire quantity on BOTH sides of the equation by that (LCD),

C. then isolate the variable to determine the value of x that makes the original equation a true statement.

Answer 1

The solution to the fraction expression is: x = -2

How to solve fraction problems?

We are given the fraction expression as:

¹/₃x - 5 = ⁵/₂x - ²/₃

The least common denominator (LCD) of all fractions in the equation is 6.

Thus, we multiply the entire quantity on BOTH sides of the equation by 6 to get:

2x - 30 = 15x - 4

Isolate the variable by rearranging the equation to get:

15x - 2x = 4 - 30

13x = -26

x -26/13

x = -2

Answer 2

The answer in the explanation

Explanation:

we have

`(1)/(3)x-5=(5)/(2)x-(2)/(3)`

Step 1

Determine the least common denominator (LCD) of all fractions in the equation

The LCD is equal to

`(3)(2)=6`

Step 2

Multiply both sides of the equation by 6 to remove the fractions

`6[(1)/(3)x-5]=6[(5)/(2)x-(2)/(3)]`

`2x-30=15x-4`

Step 3

Solve for x

Group terms

`15x-2x=-30+4`

Combine like terms

`13x=-26`

`x=-2`