Simplify x/7

x/7-1>=x/8

This deals with adding, subtracting & 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 greater equal sign from both sides of the inequality : x/7-1-(x/8)≥0

Step by step solution :

Step 1 :

x Simplify — 8Equation at the end of step 1 : x x (— - 1) - — ≥ 0 7 8

Step 2 :

x Simplify — 7Equation at the end of step 2 : x x (— - 1) - — ≥ 0 7 8

Step 3 :

Rewriting the whole as an Equivalent Fraction :3.1Subtracting a whole from a fraction Rewrite the whole as a fraction using 7 as the denominator :

1 1 • 7 1 = — = ————— 1 7 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 share the same denominator

Adding fractions that have a common denominator :3.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have sầu a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce lớn lowest terms if possible:

x - (7) x - 7 ——————— = ————— 7 7 Equation at the kết thúc of step 3 : (x - 7) x ——————— - — ≥ 0 7 8

Step 4 :

Calculating the Least Common Multiple :4.1 Find the Least Comtháng Multiple The left denominator is : 7 The right denominator is : 8

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
7101
2033
Product of allPrime Factors7856

Least Comtháng Multiple: 56

Calculating Multipliers :

4.2 Calculate multipliers for the two fractions Denote the Least Comtháng 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=8Right_M=L.C.M/R_Deno=7

Making Equivalent Fractions :

4.3 Rewrite the two fractions inlớn equivalent fractionsTwo fractions are called equivalent if they have sầu the same numeric value. For example : 1/2 & 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well. To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective sầu Multiplier.

L. Mult. • L.

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Num. (x-7) • 8 —————————————————— = ————————— L.C.M 56 R. Mult. • R. Num. x • 7 —————————————————— = ————— L.C.M 56 Adding fractions that have a common denominator :4.4 Adding up the two equivalent fractions

(x-7) • 8 - (x • 7) x - 56 ——————————————————— = —————— 56 56 Equation at the end of step 4 : x - 56 —————— ≥ 0 56

Step 5 :

5.1 Multiply both sides by 56

Solve Basic Ineunique :

5.2 Add 56 lớn both sides x ≥ 56Inequality Plot :5.3 Inequality plot for 0.018 x - 1.000 ≥ 0

One solution was found :

x ≥ 56


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