Question

7/15х+5/12(х-7/15х)+28=х

Answer 1

$\displaystyle \frac{7}{15}x+\frac{5}{12}(x-\frac{7}{15}x)+28=x\\ \\\frac{7}{15}x+\frac{5}{12}x-\frac{7}{36}x+28=x\\ \\84x+75x-35x+5040=180x\\ 124x+5040=180x\\ 124x-180x=-5040\\ -56x=-5040\\ x=90$

Answer 2

To solve the equation, let's simplify and solve step by step:

7/15x + 5/12(x - 7/15x) + 28 = x

To simplify, we'll first simplify the second term inside the parentheses:

5/12(x - 7/15x) = 5/12 * (1 - 7/15) * x = 5/12 * (15/15 - 7/15) * x = 5/12 * (8/15) * x = 40/180 * x = 2/9 * x

Now, let's substitute this simplified term back into the equation:

7/15x + 2/9x + 28 = x

To eliminate the fractions, we can multiply every term by the least common multiple (LCM) of the denominators. In this case, the LCM of 15 and 9 is 45:

45 * (7/15x) + 45 * (2/9x) + 45 * 28 = 45 * x

Simplifying further:

(45 * 7 * x) / 15 + (45 * 2 * x) / 9 + 1260 = 45x

(7 * 3 * x) / 3 + (2 * 5 * x) / 3 + 1260 = 45x

(21x + 10x) / 3 + 1260 = 45x

(31x / 3) + 1260 = 45x

Now, let's isolate the x terms on one side by subtracting (31x / 3) from both sides:

(31x / 3) - (31x / 3) + 1260 = 45x - (31x / 3)

1260 = (135x - 31x) / 3

1260 = 104x / 3

To eliminate the fraction, we can multiply both sides by 3:

3 * 1260 = 104x

3780 = 104x

Now, divide both sides by 104 to solve for x:

3780 / 104 = x

Approximately, x = 36.34615384615385.

Therefore, the solution to the equation is x ≈ 36.346.