3/4-2x/3=5x/6+1/2

This solution giao dịch with adding, subtracting and finding the least common multiple.

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Step by Step Solution

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Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3/4-2*x/3-(5*x/6+1/2)=0

Step by step solution :

Step 1 :

1 Simplify — 2Equation at the over of step 1 : 3 x x 1 (—-(2•—))-((5•—)+—) = 0 4 3 6 2

Step 2 :

x Simplify — 6Equation at the end of step 2 : 3 x x 1 (—-(2•—))-((5•—)+—) = 0 4 3 6 2

Step 3 :

Calculating the Least Common Multiple :3.1 Find the Least Common Multiple The left denominator is : 6 The right denominator is : 2

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2111
3101
Product of allPrime Factors626

Least Common Multiple: 6

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_DenoLeft_M=L.C.M/L_Deno=1Right_M=L.C.M/R_Deno=3

Making Equivalent Fractions :

3.3 Rewrite the two fractions into equivalent fractionsTwo fractions are called equivalent if they have the same numeric value. For example : 1/2 và 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well. Lớn calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 5x —————————————————— = —— L.C.M 6 R. Mult. • R. Num. 3 —————————————————— = — L.C.M 6Adding fractions that have a common denominator :3.4 Adding up the two equivalent fractions add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce lớn lowest terms if possible:

5x + 3 5x + 3 —————— = —————— 6 6 Equation at the kết thúc of step 3 : 3 x (5x + 3) (— - (2 • —)) - ———————— = 0 4 3 6

Step 4 :

x Simplify — 3Equation at the kết thúc of step 4 : 3 x (5x + 3) (— - (2 • —)) - ———————— = 0 4 3 6

Step 5 :

3 Simplify — 4Equation at the end of step 5 : 3 2x (5x + 3) (— - ——) - ———————— = 0 4 3 6

Step 6 :

Calculating the Least Common Multiple :6.1 Find the Least Common Multiple The left denominator is : 4 The right denominator is : 3

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2202
3011
Product of allPrime Factors4312

Least Common Multiple: 12

Calculating Multipliers :

6.2 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_DenoLeft_M=L.C.M/L_Deno=3Right_M=L.C.M/R_Deno=4

Making Equivalent Fractions :

6.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. 3 • 3 —————————————————— = ————— L.C.M 12 R. Mult. • R. Num. 2x • 4 —————————————————— = —————— L.C.M 12 Adding fractions that have a common denominator :6.4 Adding up the two equivalent fractions

3 • 3 - (2x • 4) 9 - 8x ———————————————— = —————— 12 12 Equation at the end of step 6 : (9 - 8x) (5x + 3) ———————— - ———————— = 0 12 6

Step 7 :

Calculating the Least Common Multiple :7.1 Find the Least Common Multiple The left denominator is : 12 The right denominator is : 6

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2212
3111
Product of allPrime Factors12612

Least Common Multiple: 12

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_DenoLeft_M=L.C.M/L_Deno=1Right_M=L.C.M/R_Deno=2

Making Equivalent Fractions :

7.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (9-8x) —————————————————— = —————— L.C.M 12 R. Mult. • R. Num.

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(5x+3) • 2 —————————————————— = —————————— L.C.M 12 Adding fractions that have a common denominator :7.4 Adding up the two equivalent fractions

(9-8x) - ((5x+3) • 2) 3 - 18x ————————————————————— = ——————— 12 12

Step 8 :

Pulling out like terms :8.1 Pull out lượt thích factors:3 - 18x=-3•(6x - 1)

Equation at the over of step 8 : -3 • (6x - 1) ————————————— = 0 12

Step 9 :

When a fraction equals zero :9.1 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:

-3•(6x-1) ————————— • 12 = 0 • 12 12 Now, on the left hand side, the 12 cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:-3 • (6x-1)=0

Equations which are never true:9.2Solve:-3=0This equation has no solution. A a non-zero constant never equals zero.

Solving a Single Variable Equation:9.3Solve:6x-1 = 0Add 1 khổng lồ both sides of the equation:6x = 1 Divide both sides of the equation by 6:x = 1/6 = 0.167