x = 0
Step-by-step explanation:
Step 1 :
5
Simplify ——
28
Equation at the end of step 1 :
4 21 1 1 5
(—•((——•x)+—))-(2•(—-(——•x))) = 0
7 8 2 7 28
Step 2 :
1
Simplify —
7
Equation at the end of step 2 :
4 21 1 1 5x
(—•((——•x)+—))-(2•(—-——)) = 0
7 8 2 7 28
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 7
The right denominator is : 28
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
7111
2022
Product of all
Prime Factors 72828
Least Common Multiple:
28
Calculating Multipliers :
3.2 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 = 4
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
3.3 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. 4
—————————————————— = ——
L.C.M 28
R. Mult. • R. Num. 5x
—————————————————— = ——
L.C.M 28
Adding fractions that have a common denominator :
3.4 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:
4 - (5x) 4 - 5x
———————— = ——————
28 28
Equation at the end of step 3 :
4 21 1 (4-5x)
(—•((——•x)+—))-(2•——————) = 0
7 8 2 28
Step 4 :
Equation at the end of step 4 :
4 21 1 (4-5x)
(—•((——•x)+—))-—————— = 0
7 8 2 14
Step 5 :
1
Simplify —
2
Equation at the end of step 5 :
4 21 1 (4-5x)
(—•((——•x)+—))-—————— = 0
7 8 2 14
Step 6 :
21
Simplify ——
8
Equation at the end of step 6 :
4 21 1 (4 - 5x)
(— • ((—— • x) + —)) - ———————— = 0
7 8 2 14
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 8
The right denominator is : 2
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2313
Product of all
Prime Factors 828
Least Common Multiple:
8
Calculating Multipliers :
7.2 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 = 1
Right_M = L.C.M / R_Deno = 4
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 21x
—————————————————— = ———
L.C.M 8
R. Mult. • R. Num. 4
—————————————————— = —
L.C.M 8
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
21x + 4 21x + 4
——————— = ———————
8 8
Equation at the end of step 7 :
4 (21x + 4) (4 - 5x)
(— • —————————) - ———————— = 0
7 8 14
Step 8 :
4
Simplify —
7
Equation at the end of step 8 :
4 (21x + 4) (4 - 5x)
(— • —————————) - ———————— = 0
7 8 14
Step 9 :
Equation at the end of step 9 :
(21x + 4) (4 - 5x)
————————— - ———————— = 0
14 14
Step 10 :
Adding fractions which have a common denominator :
10.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(21x+4) - ((4-5x)) 26x
—————————————————— = ———
14 14
Equation at the end of step 10 :
26x
——— = 0
14
Step 11 :
When a fraction equals zero :
11.1 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:
26x
——— • 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 :
26x = 0
Solving a Single Variable Equation :
11.2 Solve : 26x = 0
Divide both sides of the equation by 26:
x = 0
Hope this helps.
