This faces adding, subtracting and also finding the least usual multiple.
You are watching: X 3 18=12/9
Step by action Solution
Rearrange:Rearrange the equation by individually what is to the right of the equal sign from both political parties of the equation : x-3/18-(12/9)=0
Step by step solution :
Step 1 :
4 leveling — 3Equation in ~ the end of action 1 : 3 4 (x - ——) - — = 0 18 3
Step 2 :1 simplify — 6Equation in ~ the finish of action 2 : 1 4 (x - —) - — = 0 6 3
Step 3 :Rewriting the totality as one Equivalent portion :3.1Subtracting a fraction from a entirety Rewrite the totality as a portion using 6 as the denominator :
x x • 6 x = — = ————— 1 6 Equivalent fraction : The portion thus generated looks different yet has the very same value together the whole usual denominator : The equivalent portion and the other portion involved in the calculation re-superstructure the same denominator
Adding fountain that have actually a typical denominator :3.2 including up the two identical fractions add the two tantamount fractions which now have a typical denominatorCombine the molecule together, put the sum or difference over the usual denominator then minimize to lowest state if possible:
x • 6 - (1) 6x - 1 ——————————— = —————— 6 6 Equation in ~ the finish of action 3 : (6x - 1) 4 ———————— - — = 0 6 3
Step 4 :Calculating the Least usual Multiple :4.1 discover the Least typical Multiple The left denominator is : 6 The appropriate denominator is : 3
|Product of allPrime Factors||6||3||6|
Least common Multiple: 6Calculating multipliers :
4.2 calculation multipliers for the two fractions denote the Least common Multiple through L.C.M denote the Left Multiplier through Left_M signify the appropriate Multiplier through Right_M denote the Left Deniminator by L_Deno signify the best 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 fractions are referred to as equivalent if they have the very same numeric value. For instance : 1/2 and also 2/4 room equivalent, y/(y+1)2 and also (y2+y)/(y+1)3 are identical as well. To calculation equivalent portion , multiply the molecule of each 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 typical denominator :4.4 including up the two equivalent fractions
(6x-1) - (4 • 2) 6x - 9 ———————————————— = —————— 6 6
Step 5 :Pulling out favor terms :5.1 traction out prefer factors:6x - 9=3•(2x - 3)
Equation in ~ the finish of step 5 : 3 • (2x - 3) ———————————— = 0 6
Step 6 :When a portion equals zero :6.1 when a portion equals zero ...Where a portion equals zero, that numerator, the component which is above the fraction line, need 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, on the left hand side, the 6 cancels the end the denominator, while, top top the right hand side, zero time anything is quiet zero.The equation now takes the shape:3 • (2x-3)=0
Equations which are never ever true:6.2Solve:3=0This equation has actually no solution. A a non-zero constant never equates to zero.
Solving a single Variable Equation:6.3Solve:2x-3 = 0Add 3 to both sides of the equation:2x = 3 division both sides of the equation by 2:x = 3/2 = 1.500