Simplify ———
25
Equation at the end of step 1 :
539 112
(x + ———) - ——— > 0
100 25
Step 2 :
539
Simplify ———
100
Equation at the end of step 2 :
539 112
(x + ———) - ——— > 0
100 25
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 100 as the denominator :
x x • 100
x = — = ———————
1 100
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 a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • 100 + 539 100x + 539
————————————— = ——————————
100 100
Equation at the end of step 3 :
(100x + 539) 112
———————————— - ——— > 0
100 25
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 25
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 0 2
5 2 2 2
Product of all
Prime Factors 100 25 100
Least Common Multiple:
100
Calculating 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_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 4
Making Equivalent Fractions :
4.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 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 Multiplier.
L. Mult. • L. Num. (100x+539)
—————————————————— = ——————————
L.C.M 100
R. Mult. • R. Num. 112 • 4
—————————————————— = ———————
L.C.M 100
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
(100x+539) - (112 • 4) 100x + 91
—————————————————————— = —————————
100 100
Equation at the end of step 4 :
100x + 91
————————— > 0
100
Step 5 :
5.1 Multiply both sides by 100
5.2 Divide both sides by 100
x+(91/100) > 0
Solve Basic Inequality :
5.3 Subtract 91/100 from both sides
x > -91/100
Inequality Plot :
5.4 Inequality plot for
x + 0.910 > 0
One solution was found :
x > -91/100