Algebra
posted by Aria on .
Could someone tell me what I am doing right or wrong?
Problem Two: 5/9 + (2/9)x = 25/7 + (6/7)x – 2/3
Like signs are not collected at the beginning. This would make the equation unequal.
To make both sides equal we first multiply all sides by nine and then both sides by seven
So,
9 x 5/9 cancels out the denominator so the equation is rewritten as 5/1
9 x 2/9x does the same, so the equation is rewritten as 2/1
Now we go to the right side
Following the same principle
9 x 25/7 = 225/7
9 x 6/7x = 54/7x
9 x 2/3 = 6
We repeat the formula with seven as a multiple.
7 x 5/9 = 35/9
7 x 2/9x = 14/9x
7 x 25/7 = 175/1
7 x 6/7x = 42/1x
7 x 6 = 42
Group like numbers
5 + 2 = 175 + 42  42
Group like fractions
225/7 + 54/7x
35/9 + 14/9x
Remove denominators from like fractions
35 + 14x = 225 + 54x 42 – 42
Group like terms
14x + 54x = 68x
Group like numbers
35 + 225 – 42 = 218

5/9+(2/9)x =25/7+(6/7)x–2/3
(2/9)x(6/7)x=25/7 2/3 5/9
2/9=14/63
6/7=54/63
25/7=675/189
2/3=126/189
5/9=105/189
(2/9)x(6/7)x=25/7 2/3 5/9
(14/63)x(54/63)x=675/189 126/189 105/189
(40/63)x=444/189 Multiply with 63
40x=63*444/189
40x=27972/189 Divide with 40
x=27972/(40*189)
x= 27972/7560
27972=2*2*3*3*3*7*37
7560=2*2*2*3*3*3*5*7
x= 2*2*3*3*3*7*37/2*2*2*3*3*3*5*7
x= 37/2*5
x= 37/10
x= 3.7