Final answer:
To solve the equation x + 2/7 = 5x + 7/9, we combined like terms, found a common denominator, eliminated the fractions, and then solved for x to find the solution x = -31/252.
Step-by-step explanation:
To solve the equation x + 2/7 = 5x + 7/9, first, we want to get all the x terms on one side, and to do this, we need to isolate x. We can subtract 5x from both sides:
x - 5x + 2/7 = 7/9
Combining like terms, we get:
-4x + 2/7 = 7/9
Next, we want to get rid of the fractions by finding a common denominator, which would be 63 in this case. We multiply each term by 63 to eliminate the denominators:
63(-4x) + 63(2/7) = 63(7/9)
-252x + 18 = 49
Now, subtract 18 from both sides:
-252x = 49 - 18
-252x = 31
Finally, divide both sides by -252 to solve for x:
x = 31/-252
After simplifying the fraction, we get the solution:
x = -31/252