### 2:3=6:x

This faces including, subtracting and also finding the least widespread multiple.

You are watching: (2/3)^6

## Step by Tip Solution ### Rearrange:

Rearvariety the equation by subtracting what is to the ideal of the equal authorize from both sides of the equation : 2/3-(6/x)=0

## Step 1 :

6 Simplify — xEquation at the end of action 1 : 2 6 — - — = 0 3 x

## Tip 2 :

2 Simplify — 3Equation at the finish of action 2 : 2 6 — - — = 0 3 x

## Tip 3 :

Calculating the Leastern Common Multiple :3.1 Find the Least Typical Multiple The left denominator is : 3 The appropriate denominator is : x

Number of times each prime factorshows up in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
3101
Product of allPrime Factors313

Number of times each Algebraic Factorappears in the factorization of:AlgebraicFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
x011

Leastern Common Multiple: 3x

Calculating Multipliers :

3.2 Calculate multipliers for the 2 fractions Denote the Leastern Typical 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_DenoLeft_M=L.C.M/L_Deno=xRight_M=L.C.M/R_Deno=3

Making Equivalent Fractions :

3.3 Recreate the two fractions right into identical fractionsTwo fractions are called indistinguishable if they have actually the same numeric value. For instance : 1/2 and also 2/4 are indistinguishable, y/(y+1)2 and also (y2+y)/(y+1)3 are tantamount also. To calculate equivalent fraction , multiply the Numerator of each fractivity, by its corresponding Multiplier.

L. Mult. • L. Num. 2 • x —————————————————— = ————— L.C.M 3x R. Mult. • R. Num.

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6 • 3 —————————————————— = ————— L.C.M 3x Adding fractions that have a prevalent denominator :3.4 Adding up the two indistinguishable fractions Add the two tantamount fractions which now have a common denominatorCombine the numerators together, put the amount or distinction over the prevalent denominator then mitigate to lowest terms if possible:

2 • x - (6 • 3) 2x - 18 ——————————————— = ——————— 3x 3x

## Step 4 :

Pulling out like terms :4.1 Pull out choose factors:2x - 18=2•(x - 9)

Equation at the end of action 4 : 2 • (x - 9) ——————————— = 0 3x

## Step 5 :

When a fraction amounts to zero :5.1 When a fraction equates to zero ...Wright here a fraction equates to zero, its numerator, the part which is above the fractivity 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:

2•(x-9) ——————— • 3x = 0 • 3x 3x Now, on the left hand side, the 3x cancels out the denominator, while, on the best hand also side, zero times anything is still zero.The equation now takes the shape:2 • (x-9)=0

Equations which are never true:5.2Solve:2=0This equation has actually no solution. A a non-zero consistent never before amounts to zero.

Solving a Single Variable Equation:5.3Solve:x-9 = 0Add 9 to both sides of the equation:x = 9