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): "43.7" was replaced by "(437/10)". 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 :
(19/10)*((23/10)*n+6)+(1045/100)-((437/10))>0
Step by step solution :
Step 1 :
437
Simplify ———
10
Equation at the end of step 1 :
19 23 1045 437
((——•((——•n)+6))+————)-——— > 0
10 10 100 10
Step 2 :
209
Simplify ———
20
Equation at the end of step 2 :
19 23 209 437
((——•((——•n)+6))+———)-——— > 0
10 10 20 10
Step 3 :
23
Simplify ——
10
Equation at the end of step 3 :
19 23 209 437
((——•((——•n)+6))+———)-——— > 0
10 10 20 10
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 10 as the denominator :
6 6 • 10
6 = — = ——————
1 10
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 :
4.2 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:
23n + 6 • 10 23n + 60
———————————— = ————————
10 10
Equation at the end of step 4 :
19 (23n + 60) 209 437
((—— • ——————————) + ———) - ——— > 0
10 10 20 10
Step 5 :
19
Simplify ——
10
Equation at the end of step 5 :
19 (23n + 60) 209 437
((—— • ——————————) + ———) - ——— > 0
10 10 20 10
Step 6 :
Equation at the end of step 6 :
19 • (23n + 60) 209 437
(——————————————— + ———) - ——— > 0
100 20 10
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 20
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 2 | 2 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 100 | 20 | 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 = 5
Making Equivalent Fractions :
7.3 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. 19 • (23n+60) —————————————————— = ————————————— L.C.M 100 R. Mult. • R. Num. 209 • 5 —————————————————— = ——————— L.C.M 100
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
19 • (23n+60) + 209 • 5 437n + 2185
——————————————————————— = ———————————
100 100
Equation at the end of step 7 :
(437n + 2185) 437
————————————— - ——— > 0
100 10
Step 8 :
Step 9 :
Pulling out like terms :
9.1 Pull out like factors :
437n + 2185 = 437 • (n + 5)
Calculating the Least Common Multiple :
9.2 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 100 | 10 | 100 |
Least Common Multiple:
100
Calculating Multipliers :
9.3 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 = 10
Making Equivalent Fractions :
9.4 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 437 • (n+5) —————————————————— = ——————————— L.C.M 100 R. Mult. • R. Num. 437 • 10 —————————————————— = ———————— L.C.M 100
Adding fractions that have a common denominator :
9.5 Adding up the two equivalent fractions
437 • (n+5) - (437 • 10) 437n - 2185
———————————————————————— = ———————————
100 100
Step 10 :
Pulling out like terms :
10.1 Pull out like factors :
437n - 2185 = 437 • (n - 5)
Equation at the end of step 10 :
437 • (n - 5)
————————————— > 0
100
Step 11 :
11.1 Multiply both sides by 100
11.2 Divide both sides by 437
Solve Basic Inequality :
11.3 Add 5 to both sides
n > 5
Inequality Plot :
11.4 Inequality plot for
4.370 X - 21.850 > 0
One solution was found :
n > 5How did we do?
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