8/9 x + 2/3 x = 1/9 x + 45
multiply each term by 9
8x + 6x = x + 405
13x = 405
x = 405/13
Just a correction 8x+6x= 14x
Not 13x
So it would be 405/14 =28.9 or 29
David, there was an x on the right side, so it is 13x
To solve the given equation, we need to simplify and isolate the variable x. The equation is:
8/9 x + 2/3 x = 1/9 x + 45
First, let's combine the terms with x on both sides of the equation. To do this, we find a common denominator for the fractions and then add or subtract them accordingly.
The common denominator for 9, 3, and 1 is 9. So, we can rewrite the equation as:
(8/9 + 2/3 - 1/9) x = 45
To add fractions, we need a common denominator. In this case, it's 9. Let's find the equivalent fractions with 9 as the denominator:
(8/9 + 2/3 - 1/9) x = 45
[(8/9 * 1/1) + (2/3 * 3/3) - (1/9 * 3/3)] x = 45
(8/9 * 1/1 + 6/9 - 3/9) x = 45
(8/9 + 6/9 - 3/9) x = 45
Now, we can add the fractions with the same denominator:
(14/9) x = 45
To isolate x, we need to multiply both sides of the equation by the reciprocal of (14/9), which is (9/14). This will cancel out the fraction on the left side, and we will be left with:
[(14/9) x] * (9/14) = 45 * (9/14)
The (14/9) and (9/14) fractions cancel out, leaving us with:
x = 45 * (9/14)
Now, we can simplify the right side of the equation:
x = 45 * (9/14)
To multiply fractions, we multiply the numerators and denominators:
x = (45 * 9) / 14
x = 405 / 14
At this point, we have the exact answer as a fraction, 405/14. If we need a decimal approximation, we can divide 405 by 14:
x ≈ 28.9286
Therefore, the solution to the equation is approximately x ≈ 28.9286 or as a fraction x = 405/14.