Question 1167524
the equation is x + 1/2 * x = 10


strategy is as follows:


place all values of x under a common denominator.


x + 1/2 * x = 10 becomes 2/2 * x + 1/2 * x = 10


combine like terms.


2/2 * x + 1/2 * x = 10 becomes 3/2 * x = 10


multiply both sides of the equation by the reciprocal of the fraction.


3/2 * x = 10 becomes 2/3 * 3/2 * x = 2/3 * 10


simplify the equation by performing the operations indicated.


2/3 * 3/2 * x = 2/3 * 10 becomes x = 20/3


confirm the solution is correct by replacing the value of x with its value.


x + 1/2 * x = 10 becomes 20/3 + 1/2 * 20/3 = 10


simplify the equation further by performing the operations indicated.


20/3 + 1/2 * 20/3 = 10 becomes 20/3 + 10/3 = 10


combine like terms.


20/3 + 10/3 = 10 becomes 30/3 = 10


perform a final simplification.


30/3 = 10 becomes 10 = 10


test to see if the equation is true.


10 = 10 is true.


report the solution.


x = 20/3