x=42
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4/7*x+5/14*x-(39)=0
Simplify 5/14
((4/7• x) + (5/14 • x)) - 39 = 0
Simplify 4/7
4 5x
((— • x) + ——) - 39 = 0
7 14
Find the Least Common Multiple
The left denominator is : 7
The right denominator is : 14
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
7111
2011
Product of all
Prime Factors 71414
Least Common Multiple:
14
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 = 2
Right_M = L.C.M / R_Deno = 1
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
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. 4x • 2
—————————————————— = ——————
L.C.M 14
R. Mult. • R. Num. 5x
—————————————————— = ——
L.C.M 14
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:
4x • 2 + 5x 13x
——————————— = ———
14 14
13x
——— - 39 = 0
14
Subtracting a whole from a fraction
Rewrite the whole as a fraction using 14 as the denominator :
39 39 • 14
39 = —— = ———————
1 14
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
Adding up the two equivalent fractions
13x - (39 • 14) 13x - 546
——————————————— = —————————
14 14
Pull out like factors :
13x - 546 = 13 • (x - 42)
13 • (x - 42)
————————————— = 0
14
When a fraction equals zero ...
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:
13•(x-42)
————————— • 14 = 0 • 14
14
Now, on the left hand side, the 14 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
13 • (x-42) = 0
Solve : 13 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solve : x-42 = 0
Add 42 to both sides of the equation :
x = 42
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