Question 1197889
let x be the number.
3/4 * x -5/12 * x = 5/6 * x - 7.
3/4 * 3/3 = 9/12
5/6 * 2/2 = 10/12
equation becomes:
9/12 * x - 5/12 * x = 10/12 * x - 7
subtract 10/12 * x from both sides of the equation to get:
9/12 * x - 5/12 * x - 10/12 * x = - 7
combine like terms to get:
-6/12 * x = -7
multiply both sides of this equation by -12/6 to get:
x = -7 * -12/6
simplify to ge t:
x = 84/6 = 14


to confirm, replace x with that and evaluate the original equation.
you will get:
3/4 * x -5/12 * x = 5/6 * x - 7. becomes:
3/4 * 14 - 5/12 * 14 = 5/6 * 14 - 7
since 3/4 = 9/12 and 5/6 = 10/12 and 7 = 84/12, you get:
9/12 * 14 - 5/12 * 14 = 10/12 * 14 - 84/12
subtract 10/12 * 14 from both sides of the equation to get:
9/12 * 14 - 5/12 * 14 - 10/12 * 14 = -84/12
factor out the 14 on the left side of the equation to get:
14 * (9/12 - 5/12 - 10/12) = -84/12 which becomes:
14 * (-6/12) = -84/12 which becomes:
-84/12 = -84/12 which is true.
this confirms the value of x is good.


another way is to use your calculator on the original expressions on each side of the equal sign after replacing x with 14.
you will get:
3/4 * 14 - 5/12 * 14 = -4.666666.....
5/6 * 14 - 7 = -4.66666.....
since the expression on the left side of the equal sign is equal to the expression on the right side of the equal sign, the equation is true and the value of x is good.


your solution is that the number is equal to 14.