This faces adding, subtracting and finding the least usual multiple.
You are watching: X 3 18=12/9
Step by step Solution
Rearrange:Rearrange the equation by individually what is to the right of the equal authorize from both political parties of the equation : x-3/18-(12/9)=0
Step by action solution :
Step 1 :
4 leveling — 3Equation in ~ the end of step 1 : 3 4 (x - ——) - — = 0 18 3
Step 2 :1 leveling — 6Equation at the end of action 2 : 1 4 (x - —) - — = 0 6 3
Step 3 :Rewriting the totality as one Equivalent portion :3.1Subtracting a portion from a whole Rewrite the entirety as a portion using 6 together the denominator :
x x • 6 x = — = ————— 1 6 Equivalent portion : The portion thus produced looks different yet has the very same value together the whole common denominator : The equivalent fraction and the other portion involved in the calculation share the same denominator
Adding fractions that have a common denominator :3.2 adding up the two tantamount fractions include the two tantamount fractions i beg your pardon now have a common denominatorCombine the molecule together, put the amount or distinction over the common denominator then minimize to lowest terms if possible:
x • 6 - (1) 6x - 1 ——————————— = —————— 6 6 Equation in ~ the end of action 3 : (6x - 1) 4 ———————— - — = 0 6 3
Step 4 :Calculating the Least typical Multiple :4.1 discover the Least common Multiple The left denominator is : 6 The appropriate denominator is : 3
|Product that allPrime Factors||6||3||6|
Least usual Multiple: 6Calculating multipliers :
4.2 calculate multipliers for the 2 fractions signify the Least common Multiple by L.C.M represent the Left Multiplier by Left_M denote the ideal Multiplier by Right_M represent the Left Deniminator through L_Deno denote the ideal Multiplier by R_DenoLeft_M=L.C.M/L_Deno=1Right_M=L.C.M/R_Deno=2Making tantamount Fractions :
4.3 Rewrite the two fractions into indistinguishable fractionsTwo fountain are referred to as equivalent if they have the exact same numeric value. For instance : 1/2 and also 2/4 space equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are tantamount as well. To calculation equivalent fraction , main point the molecule of every fraction, by its particular Multiplier.
L. Mult. • L. Num. (6x-1) —————————————————— = —————— L.C.M 6 R. Mult. • R. Num.
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4 • 2 —————————————————— = ————— L.C.M 6 adding fractions that have actually a common denominator :4.4 adding up the two tantamount fractions
(6x-1) - (4 • 2) 6x - 9 ———————————————— = —————— 6 6
Step 5 :Pulling out choose terms :5.1 pull out choose factors:6x - 9=3•(2x - 3)
Equation in ~ the end of action 5 : 3 • (2x - 3) ———————————— = 0 6
Step 6 :When a portion equals zero :6.1 when a fraction equals zero ...Where a fraction equals zero, that numerator, the part which is over the portion line, have to equal zero.Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.Here"s how:
3•(2x-3) ———————— • 6 = 0 • 6 6 Now, top top the left hand side, the 6 cancels out the denominator, while, top top the right hand side, zero times anything is tho zero.The equation currently takes the shape:3 • (2x-3)=0
Equations which are never ever true:6.2Solve:3=0This equation has no solution. A a non-zero constant never equates to zero.
Solving a single Variable Equation:6.3Solve:2x-3 = 0Add 3 to both political parties of the equation:2x = 3 division both sides of the equation through 2:x = 3/2 = 1.500