This solution giao dịch with adding, subtracting and finding the least common multiple.
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Step by Step Solution
Rearrange:Rearrange the equation by subtracting what is khổng lồ the right of the equal sign from both sides of the equation : 2*x-3/4-(1/2)=0
Step by step solution :
Step 1 :
1 Simplify — 2Equation at the end of step 1 : 3 1 (2x - —) - — = 0 4 2
Step 2 :3 Simplify — 4Equation at the kết thúc of step 2 : 3 1 (2x - —) - — = 0 4 2
Step 3 :Rewriting the whole as an Equivalent Fraction :3.1Subtracting a fraction from a whole Rewrite the whole as a fraction using 4 as the denominator :
2x 2x • 4 2x = —— = —————— 1 4 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 share the same denominator
Adding fractions that have a common denominator :3.2 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 to lowest terms if possible:
2x • 4 - (3) 8x - 3 ———————————— = —————— 4 4 Equation at the over of step 3 : (8x - 3) 1 ———————— - — = 0 4 2
Step 4 :Calculating the Least Common Multiple :4.1 Find the Least Common Multiple The left denominator is : 4 The right denominator is : 2
|Product of allPrime Factors||4||2||4|
Least Common Multiple: 4Calculating 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=1Right_M=L.C.M/R_Deno=2Making 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 & (y2+y)/(y+1)3 are equivalent as well. To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (8x-3) —————————————————— = —————— L.C.M 4 R. Mult. • R.
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Num. 2 —————————————————— = — L.C.M 4Adding fractions that have a common denominator :4.4 Adding up the two equivalent fractions
(8x-3) - (2) 8x - 5 ———————————— = —————— 4 4 Equation at the kết thúc of step 4 : 8x - 5 —————— = 0 4
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:
8x-5 ———— • 4 = 0 • 4 4 Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:8x-5=0
Solving a Single Variable Equation:5.2Solve:8x-5 = 0Add 5 to both sides of the equation:8x = 5 Divide both sides of the equation by 8:x = 5/8 = 0.625