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): "38.74" was replaced by "(3874/100)". 4 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 :
(354/10)*d-(8179/100)-((359/10)*d-(3874/100))>0
Step by step solution :
Step 1 :
1937
Simplify ————
50
Equation at the end of step 1 :
354 8179 359 1937
((———•d)-————)-((———•d)-————) > 0
10 100 10 50
Step 2 :
359
Simplify ———
10
Equation at the end of step 2 :
354 8179 359 1937
((———•d)-————)-((———•d)-————) > 0
10 100 10 50
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 50
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 1 | 1 |
| 5 | 1 | 2 | 2 |
| Product of all Prime Factors | 10 | 50 | 50 |
Least Common Multiple:
50
Calculating Multipliers :
3.2 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 = 5
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
3.3 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. 359d • 5 —————————————————— = ———————— L.C.M 50 R. Mult. • R. Num. 1937 —————————————————— = ———— L.C.M 50
Adding fractions that have a common denominator :
3.4 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:
359d • 5 - (1937) 1795d - 1937
————————————————— = ————————————
50 50
Equation at the end of step 3 :
354 8179 (1795d - 1937)
((——— • d) - ————) - —————————————— > 0
10 100 50
Step 4 :
8179
Simplify ————
100
Equation at the end of step 4 :
354 8179 (1795d - 1937)
((——— • d) - ————) - —————————————— > 0
10 100 50
Step 5 :
177
Simplify ———
5
Equation at the end of step 5 :
177 8179 (1795d - 1937)
((——— • d) - ————) - —————————————— > 0
5 100 50
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 2 | 2 |
| 2 | 0 | 2 | 2 |
| Product of all Prime Factors | 5 | 100 | 100 |
Least Common Multiple:
100
Calculating Multipliers :
6.2 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 = 20
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 177d • 20 —————————————————— = ————————— L.C.M 100 R. Mult. • R. Num. 8179 —————————————————— = ———— L.C.M 100
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
177d • 20 - (8179) 3540d - 8179
—————————————————— = ————————————
100 100
Equation at the end of step 6 :
(3540d - 8179) (1795d - 1937)
—————————————— - —————————————— > 0
100 50
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 50
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 2 | 2 | 2 |
| Product of all Prime Factors | 100 | 50 | 100 |
Least Common Multiple:
100
Calculating Multipliers :
7.2 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 = 2
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (3540d-8179) —————————————————— = ———————————— L.C.M 100 R. Mult. • R. Num. (1795d-1937) • 2 —————————————————— = ———————————————— L.C.M 100
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
(3540d-8179) - ((1795d-1937) • 2) -50d - 4305
————————————————————————————————— = ———————————
100 100
Step 8 :
Pulling out like terms :
8.1 Pull out like factors :
-50d - 4305 = -5 • (10d + 861)
Equation at the end of step 8 :
-5 • (10d + 861)
———————————————— > 0
100
Step 9 :
9.1 Multiply both sides by 100
9.2 Divide both sides by -5
Remember to flip the inequality sign:
9.3 Divide both sides by 10
d+(861/10) < 0
Solve Basic Inequality :
9.4 Subtract 861/10 from both sides
d < -861/10
Inequality Plot :
9.5 Inequality plot for
-0.500 X - 43.050 < 0
One solution was found :
d < -861/10How did we do?
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