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): "1.25" was replaced by "(125/100)". 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 :
(15/10)*(c)+(125/100)-(89/12)>0
Step by step solution :
Step 1 :
89
Simplify ——
12
Equation at the end of step 1 :
15 125 89
((—— • c) + ———) - —— > 0
10 100 12
Step 2 :
5
Simplify —
4
Equation at the end of step 2 :
15 5 89
((—— • c) + —) - —— > 0
10 4 12
Step 3 :
3
Simplify —
2
Equation at the end of step 3 :
3 5 89
((— • c) + —) - —— > 0
2 4 12
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 4
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| Product of all Prime Factors | 2 | 4 | 4 |
Least Common Multiple:
4
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 = 2
Right_M = L.C.M / R_Deno = 1
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. 3c • 2 —————————————————— = —————— L.C.M 4 R. Mult. • R. Num. 5 —————————————————— = — L.C.M 4
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:
3c • 2 + 5 6c + 5
—————————— = ——————
4 4
Equation at the end of step 4 :
(6c + 5) 89
———————— - —— > 0
4 12
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 4
The right denominator is : 12
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 2 | 2 |
| 3 | 0 | 1 | 1 |
| Product of all Prime Factors | 4 | 12 | 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 = 3
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (6c+5) • 3 —————————————————— = —————————— L.C.M 12 R. Mult. • R. Num. 89 —————————————————— = —— L.C.M 12
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(6c+5) • 3 - (89) 18c - 74
————————————————— = ————————
12 12
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
18c - 74 = 2 • (9c - 37)
Equation at the end of step 6 :
2 • (9c - 37)
————————————— > 0
12
Step 7 :
7.1 Multiply both sides by 12
7.2 Divide both sides by 2
7.3 Divide both sides by 9
c-(37/9) > 0
Solve Basic Inequality :
7.4 Add 37/9 to both sides
c > 37/9
Inequality Plot :
7.5 Inequality plot for
1.500 X - 6.167 > 0
One solution was found :
c > 37/9How did we do?
Please leave us feedback.