We are given equation:
5/6 x -2 = -2/3 x +1.
Note: when we have fracions in an equation, we always try to get rid fractions by removing denominator parts.
In the given equation we have 6 and 3 in denominator. So, we need to find the common denominator (lowest common denomiantor) of 6 and 3.
The lowest common denomiantor of 6 and 3 is 6.
So, equation is being multiplied by 6 on both sides.
Therefore,
Step 1) Multiply each side by LCD of fractions.
6 ( 5/6 x -2 ) = 6 (-2/3 x +1)
Step 2) Use distributive property to simplify above step, we get
6* 5/6 x = 5x
6 * -2 = -12
6 * -2/3 x = -4x and
6 * 1 = 6.
Therefore, we get
5x - 12 = -4x + 6 on simplifying second step.
Step 3) We use Addition property of Equality in third step.
Because we have -4x on right side, and the reverse operation of subtraction is addition.
5x - 12 = -4x + 6
+4x +4x Step 4) Here we just did simplification of above step.
____________________
9x -12 = 6
+12 +12 Step 5) Again applied Addition property of Equality to get rid -12 from left side.
_______________
9x = 18 Step 6) Here we just did simplification of above step.
Step 7) Because 9 is being multiplied with x on left side. To get rid 9 from left side we need to apply reverse operation of multiplication.
Therefore, Division property of equality is used there by dividing 9 on both sides.
9x/9 = 18/9
Step 8) Again did simplification of above step.
x=2 Final answer.
