4/5x-3/4x=3/10x-1
This solution giao dịch with adding, subtracting và finding the least common multiple.
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Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to lớn the right of the equal sign from both sides of the equation : 4/5*x-3/4*x-(3/10*x-1)=0Step by step solution :
Step 1 :
3 Simplify —— 10Equation at the end of step 1 : 4 3 3 ((—•x)-(—•x))-((——•x)-1) = 0 5 4 10
Step 2 :
Rewriting the whole as an Equivalent Fraction :2.1Subtracting a whole from a fraction Rewrite the whole as a fraction using 10 as the denominator :1 1 • 10 1 = — = —————— 1 10 Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation mô tả the same denominator
Adding fractions that have a common denominator :2.2 Adding up the two equivalent fractions địa chỉ cửa hàng 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:
3x - (10) 3x - 10 ————————— = ——————— 10 10 Equation at the over of step 2 : 4 3 (3x-10) ((—•x)-(—•x))-——————— = 0 5 4 10
Step 3 :
3 Simplify — 4Equation at the kết thúc of step 3 : 4 3 (3x - 10) ((— • x) - (— • x)) - ————————— = 0 5 4 10Step 4 :
4 Simplify — 5Equation at the over of step 4 : 4 3x (3x - 10) ((— • x) - ——) - ————————— = 0 5 4 10Step 5 :
Calculating the Least Common Multiple :5.1 Find the Least Common Multiple The left denominator is : 5 The right denominator is : 4| 5 | 1 | 0 | 1 |
| 2 | 0 | 2 | 2 |
| Product of allPrime Factors | 5 | 4 | 20 |
Least Common Multiple: 20
Calculating Multipliers :5.2 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 :5.3 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 và (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. 4x • 4 —————————————————— = —————— L.C.M 20 R. Mult. • R. Num. 3x • 5 —————————————————— = —————— L.C.M đôi mươi Adding fractions that have a common denominator :5.4 Adding up the two equivalent fractions
4x • 4 - (3x • 5) x ————————————————— = —— 20 20Equation at the over of step 5 : x (3x - 10) —— - ————————— = 0 20 10
Step 6 :
Calculating the Least Common Multiple :6.1 Find the Least Common Multiple The left denominator is : đôi mươi The right denominator is : 10| 2 | 2 | 1 | 2 |
| 5 | 1 | 1 | 1 |
| Product of allPrime Factors | 20 | 10 | 20 |
Least Common Multiple: 20
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=1Right_M=L.C.M/R_Deno=2
Making Equivalent Fractions :6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. X —————————————————— = —— L.C.M 20 R. Mult. • R. Num.
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(3x-10) • 2 —————————————————— = ——————————— L.C.M 20 Adding fractions that have a common denominator :6.4 Adding up the two equivalent fractions
x - ((3x-10) • 2) đôi mươi - 5x ————————————————— = ——————— trăng tròn 20
Step 7 :
Pulling out lượt thích terms :7.1 Pull out lượt thích factors:20 - 5x=-5•(x - 4)Equation at the over of step 7 : -5 • (x - 4) ———————————— = 0 đôi mươi
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:-5•(x-4) ———————— • trăng tròn = 0 • 20 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:-5 • (x-4)=0
Equations which are never true:8.2Solve:-5=0This equation has no solution. A a non-zero constant never equals zero.
Solving a Single Variable Equation:8.3Solve:x-4 = 0Add 4 khổng lồ both sides of the equation:x = 4