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

This solution giao dịch with adding, subtracting & 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 lớn the right of the equal sign from both sides of the equation : 1/2*x-1/3-(1/4*x-1/5)=0

Step by step solution :

Step 1 :

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

Step 2 :

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

Step 3 :

Calculating the Least Common Multiple :3.1 Find the Least Common Multiple The left denominator is : 4 The right denominator is : 5

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2202
5011
Product of allPrime Factors4520

Least Common Multiple: 20

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=5Right_M=L.C.M/R_Deno=4

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 & (y2+y)/(y+1)3 are equivalent as well. Khổng lồ calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. X • 5 —————————————————— = ————— L.C.M 20 R. Mult. • R. Num. 4 —————————————————— = —— L.C.M 20Adding fractions that have a common denominator :3.4 Adding up the two equivalent fractions địa chỉ the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lớn lowest terms if possible:

x • 5 - (4) 5x - 4 ——————————— = —————— trăng tròn 20 Equation at the over of step 3 : 1 1 (5x - 4) ((— • x) - —) - ———————— = 0 2 3 20

Step 4 :

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

Step 5 :

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

Step 6 :

Calculating the Least Common Multiple :6.1 Find the Least Common Multiple The left denominator is : 2 The right denominator is : 3

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2101
3011
Product of allPrime Factors236

Least Common Multiple: 6

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=2

Making Equivalent Fractions :

6.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. X • 3 —————————————————— = ————— L.C.M 6 R. Mult. • R. Num. 2 —————————————————— = — L.C.M 6Adding fractions that have a common denominator :6.4 Adding up the two equivalent fractions

x • 3 - (2) 3x - 2 ——————————— = —————— 6 6 Equation at the over of step 6 : (3x - 2) (5x - 4) ———————— - ———————— = 0 6 20

Step 7 :

Calculating the Least Common Multiple :7.1 Find the Least Common Multiple The left denominator is : 6 The right denominator is : 20

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2122
3101
5011
Product of allPrime Factors62060

Least Common Multiple: 60

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=10Right_M=L.C.M/R_Deno=3

Making Equivalent Fractions :

7.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (3x-2) • 10 —————————————————— = ——————————— L.C.M 60 R. Mult. • R.

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Num. (5x-4) • 3 —————————————————— = —————————— L.C.M 60 Adding fractions that have a common denominator :7.4 Adding up the two equivalent fractions

(3x-2) • 10 - ((5x-4) • 3) 15x - 8 —————————————————————————— = ——————— 60 60 Equation at the end of step 7 : 15x - 8 ——————— = 0 60

Step 8 :

When a fraction equals zero :8.1 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:

15x-8 ————— • 60 = 0 • 60 60 Now, on the left hand side, the 60 cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:15x-8=0

Solving a Single Variable Equation:8.2Solve:15x-8 = 0Add 8 to both sides of the equation:15x = 8 Divide both sides of the equation by 15:x = 8/15 = 0.533