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): "14.6" was replaced by "(146/10)". 2 more similar replacement(s)
Rearrange:
Rearrange the equation by subtracting what is to the right of the less equal sign from both sides of the inequality :
5/11*n-(104/10)-((146/10))≤0
Step by step solution :
Step 1 :
73
Simplify ——
5
Equation at the end of step 1 :
5 104 73
((—— • n) - ———) - —— ≤ 0
11 10 5
Step 2 :
52
Simplify ——
5
Equation at the end of step 2 :
5 52 73
((—— • n) - ——) - —— ≤ 0
11 5 5
Step 3 :
5
Simplify ——
11
Equation at the end of step 3 :
5 52 73
((—— • n) - ——) - —— ≤ 0
11 5 5
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 11
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 11 | 1 | 0 | 1 |
| 5 | 0 | 1 | 1 |
| Product of all Prime Factors | 11 | 5 | 55 |
Least Common Multiple:
55
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 = 5
Right_M = L.C.M / R_Deno = 11
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. 5n • 5 —————————————————— = —————— L.C.M 55 R. Mult. • R. Num. 52 • 11 —————————————————— = ——————— L.C.M 55
Adding fractions that have a common denominator :
4.4 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:
5n • 5 - (52 • 11) 25n - 572
—————————————————— = —————————
55 55
Equation at the end of step 4 :
(25n - 572) 73
——————————— - —— ≤ 0
55 5
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 55
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 1 | 1 |
| 11 | 1 | 0 | 1 |
| Product of all Prime Factors | 55 | 5 | 55 |
Least Common Multiple:
55
Calculating Multipliers :
5.2 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 = 11
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (25n-572) —————————————————— = ————————— L.C.M 55 R. Mult. • R. Num. 73 • 11 —————————————————— = ——————— L.C.M 55
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(25n-572) - (73 • 11) 25n - 1375
————————————————————— = ——————————
55 55
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
25n - 1375 = 25 • (n - 55)
Equation at the end of step 6 :
25 • (n - 55)
————————————— ≤ 0
55
Step 7 :
7.1 Multiply both sides by 55
7.2 Divide both sides by 25
Solve Basic Inequality :
7.3 Add 55 to both sides
n ≤ 55
Inequality Plot :
7.4 Inequality plot for
0.455 X - 25.000 ≤ 0
One solution was found :
n ≤ 55How did we do?
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