x/5=x/4-1

This solution giao dịch with adding, subtracting và 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 : x/5-(x/4-1)=0

Step by step solution :

Step 1 :

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

Step 2 :

Rewriting the whole as an Equivalent Fraction :2.1Subtracting a whole from a fraction Rewrite the whole as a fraction using 4 as the denominator :

1 1 • 4 1 = — = ————— 1 4 Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction và the other fraction involved in the calculation nói qua the same denominator

Adding fractions that have a common denominator :2.2 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 khổng lồ lowest terms if possible:

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

Step 3 :

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

Step 4 :

Calculating the Least Common Multiple :4.1 Find the Least Common Multiple The left denominator is : 5 The right denominator is : 4

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
5101
2022
Product of allPrime Factors5420

Least Common Multiple: 20

Calculating Multipliers :

4.2 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=4Right_M=L.C.M/R_Deno=5

Making Equivalent Fractions :

4.3 Rewrite the two fractions into equivalent fractionsTwo fractions are called equivalent if they have the same numeric value. For example : 1/2 and 2/4 are equivalent, y/(y+1)2 và (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. X • 4 —————————————————— = ————— L.C.M 20 R. Mult. • R.

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Num. (x-4) • 5 —————————————————— = ————————— L.C.M đôi mươi Adding fractions that have a common denominator :4.4 Adding up the two equivalent fractions

x • 4 - ((x-4) • 5) đôi mươi - x ——————————————————— = —————— trăng tròn 20 Equation at the end of step 4 : 20 - x —————— = 0 trăng tròn

Step 5 :

When a fraction equals zero :5.1 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:

20-x ———— • trăng tròn = 0 • trăng tròn 20 Now, on the left hand side, the đôi mươi cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:20-x=0

Solving a Single Variable Equation:5.2Solve:-x+20 = 0Subtract đôi mươi from both sides of the equation:-x = -20 Multiply both sides of the equation by (-1) : x = trăng tròn