x-7/8=3/4

This encounters adding, subtracting and finding the least typical multiple.




You are watching: Solve for x: 7 over 8 minus 1 over x equals 3 over 4.

Step by step Solution

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Rearrange:

Rearrange the equation by subtracting what is come the appropriate of the equal authorize from both sides of the equation : x-7/8-(3/4)=0

Step by step solution :

Step 1 :

3 leveling — 4Equation at the end of action 1 : 7 3 (x - —) - — = 0 8 4

Step 2 :

7 simplify — 8Equation at the end of action 2 : 7 3 (x - —) - — = 0 8 4

Step 3 :

Rewriting the entirety as an Equivalent portion :3.1Subtracting a fraction from a whole Rewrite the entirety as a portion using 8 together the denominator :

x x • 8 x = — = ————— 1 8 Equivalent portion : The portion thus created looks different however has the very same value as the whole typical denominator : The equivalent portion and the other portion involved in the calculation re-superstructure the same denominator

Adding fountain that have actually a typical denominator :3.2 including up the two identical fractions add the two tantamount fractions i beg your pardon now have actually a common denominatorCombine the molecule together, placed the amount or distinction over the usual denominator then mitigate to lowest terms if possible:

x • 8 - (7) 8x - 7 ——————————— = —————— 8 8 Equation in ~ the finish of action 3 : (8x - 7) 3 ———————— - — = 0 8 4

Step 4 :

Calculating the Least common Multiple :4.1 discover the Least typical Multiple The left denominator is : 8 The right denominator is : 4

Number the times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2323
Product that allPrime Factors848

Least usual Multiple: 8

Calculating multipliers :

4.2 calculation multipliers for the 2 fractions represent the Least typical Multiple by L.C.M denote the Left Multiplier by Left_M signify the best Multiplier by Right_M represent the Left Deniminator by L_Deno represent the ideal Multiplier by R_DenoLeft_M=L.C.M/L_Deno=1Right_M=L.C.M/R_Deno=2

Making tantamount Fractions :

4.3 Rewrite the two fractions into equivalent fractionsTwo fountain are called equivalent if they have actually the same numeric value. For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and also (y2+y)/(y+1)3 are tantamount as well. To calculate equivalent portion , multiply the molecule of every fraction, by its particular Multiplier.

L. Mult. • L. Num. (8x-7) —————————————————— = —————— L.C.M 8 R. Mult. • R.

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Num. 3 • 2 —————————————————— = ————— L.C.M 8 including fractions that have a typical denominator :4.4 adding up the two indistinguishable fractions

(8x-7) - (3 • 2) 8x - 13 ———————————————— = ——————— 8 8 Equation at the end of step 4 : 8x - 13 ——————— = 0 8

Step 5 :

When a fraction equals zero :5.1 once a portion equals zero ...Where a portion equals zero, its numerator, the component which is above the fraction line, must equal zero.Now,to eliminate the denominator, Tiger multiplys both sides of the equation by the denominator.Here"s how:

8x-13 ————— • 8 = 0 • 8 8 Now, ~ above the left hand side, the 8 cancels the end the denominator, while, top top the right hand side, zero times anything is quiet zero.The equation currently takes the shape:8x-13=0

Solving a solitary Variable Equation:5.2Solve:8x-13 = 0Add 13 come both political parties of the equation:8x = 13 division both sides of the equation by 8:x = 13/8 = 1.625