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): "1.5" was replaced by "(15/10)". 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 :
89/12*(c)+(125/100)-((15/10))>0
Step by step solution :
Step 1 :
3
Simplify —
2
Equation at the end of step 1 :
89 125 3
((—— • c) + ———) - — > 0
12 100 2
Step 2 :
5
Simplify —
4
Equation at the end of step 2 :
89 5 3
((—— • c) + —) - — > 0
12 4 2
Step 3 :
89
Simplify ——
12
Equation at the end of step 3 :
89 5 3
((—— • c) + —) - — > 0
12 4 2
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 12
The right denominator is : 4
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 2 | 2 |
| 3 | 1 | 0 | 1 |
| Product of all Prime Factors | 12 | 4 | 12 |
Least Common Multiple:
12
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 = 3
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. 89c —————————————————— = ——— L.C.M 12 R. Mult. • R. Num. 5 • 3 —————————————————— = ————— L.C.M 12
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:
89c + 5 • 3 89c + 15
——————————— = ————————
12 12
Equation at the end of step 4 :
(89c + 15) 3
—————————— - — > 0
12 2
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 12
The right denominator is : 2
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 3 | 1 | 0 | 1 |
| Product of all Prime Factors | 12 | 2 | 12 |
Least Common Multiple:
12
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 = 6
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (89c+15) —————————————————— = ———————— L.C.M 12 R. Mult. • R. Num. 3 • 6 —————————————————— = ————— L.C.M 12
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(89c+15) - (3 • 6) 89c - 3
—————————————————— = ———————
12 12
Equation at the end of step 5 :
89c - 3
——————— > 0
12
Step 6 :
6.1 Multiply both sides by 12
6.2 Divide both sides by 89
c-(3/89) > 0
Solve Basic Inequality :
6.3 Add 3/89 to both sides
c > 3/89
Inequality Plot :
6.4 Inequality plot for
7.417 c - 0.250 > 0
One solution was found :
c > 3/89How did we do?
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