Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "1.04" was replaced by "(104/100)". 2 more similar replacement(s)
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
3600+(102/100)*x-(2000+(104/100)*x)<0
Step by step solution :
Step 1 :
26
Simplify ——
25
Equation at the end of step 1 :
102 26
(3600+(———•x))-(2000+(——•x)) < 0
100 25
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 25 as the denominator :
2000 2000 • 25
2000 = ———— = —————————
1 25
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 :
2.2 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:
2000 • 25 + 26x 26x + 50000
——————————————— = ———————————
25 25
Equation at the end of step 2 :
102 (26x + 50000)
(3600 + (——— • x)) - ————————————— < 0
100 25
Step 3 :
51
Simplify ——
50
Equation at the end of step 3 :
51 (26x + 50000)
(3600 + (—— • x)) - ————————————— < 0
50 25
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 50 as the denominator :
3600 3600 • 50
3600 = ———— = —————————
1 50
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
3600 • 50 + 51x 51x + 180000
——————————————— = ————————————
50 50
Equation at the end of step 4 :
(51x + 180000) (26x + 50000)
—————————————— - ————————————— < 0
50 25
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
51x + 180000 = 3 • (17x + 60000)
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
26x + 50000 = 2 • (13x + 25000)
Calculating the Least Common Multiple :
7.2 Find the Least Common Multiple
The left denominator is : 50
The right denominator is : 25
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 2 | 2 | 2 |
| Product of all Prime Factors | 50 | 25 | 50 |
Least Common Multiple:
50
Calculating Multipliers :
7.3 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 = 2
Making Equivalent Fractions :
7.4 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. 3 • (17x+60000) —————————————————— = ——————————————— L.C.M 50 R. Mult. • R. Num. 2 • (13x+25000) • 2 —————————————————— = ——————————————————— L.C.M 50
Adding fractions that have a common denominator :
7.5 Adding up the two equivalent fractions
3 • (17x+60000) - (2 • (13x+25000) • 2) 80000 - x
——————————————————————————————————————— = —————————
50 50
Equation at the end of step 7 :
80000 - x
————————— < 0
50
Step 8 :
8.1 Multiply both sides by 50
8.2 Multiply both sides by (-1)
Flip the inequality sign since you are multiplying by a negative number
x-80000 > 0
Solve Basic Inequality :
8.3 Add 80000 to both sides
x > 80000
Inequality Plot :
8.4 Inequality plot for
-0.020 x + 1600.000 < 0
One solution was found :
x > 80000How did we do?
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