finding what x will equal

Question

Find any restrictions on the values of x in the equation. (Enter your answers as a comma-separated list. If there are no restrictions on x, enter NONE.)

1

2

x − 9 = 18

x ≠  

 

 

Answer 1

The equation to solve:

(1/2)x - 9 = 18 (note the grouping symbols around the 1/2. Otherwise could be interpreted as 1/(2x).

Since this equation only contains one fraction, the numerical coefficient of the unknown, it really is not necessary to clear the equation of fractions as a first step.

(1/2)x = 27 (add 9 to both sides)

x = 54 (multiply both sides by 2--the reciprocal of 1/2)

If you did clear the equation of fractions as a 1st step by multiplying every term by 2 the work would look like this:

(1/2)x - 9 =18

x - 18 = 36 (multiply every term by 2)

x = 54 (add 18 to both sides)

The choice of technique is whatever you are comfortable with.