1/5x-7/3x=1

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 lớn the right of the equal sign from both sides of the equation : 1/5*x-7/3*x-(1)=0

Step by step solution :

Step 1 :

7 Simplify — 3Equation at the kết thúc of step 1 : 1 7 ((— • x) - (— • x)) - 1 = 0 5 3

Step 2 :

1 Simplify — 5Equation at the kết thúc of step 2 : 1 7x ((— • x) - ——) - 1 = 0 5 3

Step 3 :

Calculating the Least Common Multiple :3.1 Find the Least Common Multiple The left denominator is : 5 The right denominator is : 3

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
5101
3011
Product of allPrime Factors5315

Least Common Multiple: 15

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=3Right_M=L.C.M/R_Deno=5

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 : một nửa & 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 • 3 —————————————————— = ————— L.C.M 15 R. Mult. • R.

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Num. 7x • 5 —————————————————— = —————— L.C.M 15 Adding fractions that have a common denominator :3.4 Adding up the two equivalent fractions showroom 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:

x • 3 - (7x • 5) -32x ———————————————— = ———— 15 15 Equation at the kết thúc of step 3 : -32x ———— - 1 = 0 15

Step 4 :

Rewriting the whole as an Equivalent Fraction :4.1Subtracting a whole from a fraction Rewrite the whole as a fraction using 15 as the denominator :

1 1 • 15 1 = — = —————— 1 15 Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction & the other fraction involved in the calculation chia sẻ the same denominator

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

-32x - (15) -32x - 15 ——————————— = ————————— 15 15

Step 5 :

Pulling out like terms :5.1 Pull out lượt thích factors:-32x - 15=-1•(32x + 15)

Equation at the over of step 5 : -32x - 15 ————————— = 0 15

Step 6 :

When a fraction equals zero :6.1 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:

-32x-15 ——————— • 15 = 0 • 15 15 Now, on the left hand side, the 15 cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:-32x-15=0

Solving a Single Variable Equation:6.2Solve:-32x-15 = 0Add 15 khổng lồ both sides of the equation:-32x = 15 Multiply both sides of the equation by (-1) : 32x = -15 Divide both sides of the equation by 32:x = -15/32 = -0.469