Sagot :
Réponse :
Bonjour, Hi
x = 32/19 = 1.684
Explication étape par étape
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(7*x+1)/9+(3*x-1)/7-(2)=0
3x - 1
Simplify ——————
7
(7x + 1) (3x - 1)
(———————— + ————————) - 2 = 0
9 7
7x + 1
Simplify ——————
9
(7x + 1) (3x - 1)
(———————— + ————————) - 2 = 0
9 7
Find the Least Common Multiple
- The left denominator is : 9
- The right denominator is : 7
Least Common Multiple : 63
Calculate multipliers for the two fractions
- Denote the Least Common Multiple by L.C.M
- Denote the Left Multiplier by Left_M
- Denote the Right Multiplier by Right_M
- Denote the Left Deniminator by L_Deno
- Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 7
Right_M = L.C.M / R_Deno = 9
Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. * L. Num. (7x+1) * 7
—————————————————— = ——————————
L.C.M 63
R. Mult. * R. Num. (3x-1) • 9
—————————————————— = ——————————
L.C.M 63
Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(7x+1) • 7 + (3x-1) • 9 76x - 2
——————————————————————— = ———————
63 63
(76x - 2)
————————— - 2 = 0
63
Rewrite the whole as a fraction using 63 as the denominator :
2 2 * 63
2 = — = ——————
1 63
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Pull out like factors :
76x - 2 = 2 * (38x - 1)
Adding up the two equivalent fractions
2 • (38x-1) - (2 • 63) 76x - 128
—————————————————————— = —————————
63 63
Pull out like factors :
76x - 128 = 4 • (19x - 32)
4 * (19x - 32)
—————————————— = 0
63
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
4•(19x-32)
—————————— * 63 = 0 * 63 = 0
63
Now, on the left hand side, the 63 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
4 * (19x-32) = 0
Solve : 4 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solve : 19x-32 = 0
Add 32 to both sides of the equation :
19x = 32
Divide both sides of the equation by 19:
x = 32/19 = 1.684
