Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
c-3/7-(6/13)<0
Step by step solution :
Step 1 :
6
Simplify ——
13
Equation at the end of step 1 :
3 6
(c - —) - —— < 0
7 13
Step 2 :
3
Simplify —
7
Equation at the end of step 2 :
3 6
(c - —) - —— < 0
7 13
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 7 as the denominator :
c c • 7
c = — = —————
1 7
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 :
3.2 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:
c • 7 - (3) 7c - 3
——————————— = ——————
7 7
Equation at the end of step 3 :
(7c - 3) 6
———————— - —— < 0
7 13
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 7
The right denominator is : 13
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 7 | 1 | 0 | 1 |
| 13 | 0 | 1 | 1 |
| Product of all Prime Factors | 7 | 13 | 91 |
Least Common Multiple:
91
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 = 13
Right_M = L.C.M / R_Deno = 7
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. (7c-3) • 13 —————————————————— = ——————————— L.C.M 91 R. Mult. • R. Num. 6 • 7 —————————————————— = ————— L.C.M 91
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
(7c-3) • 13 - (6 • 7) 91c - 81
————————————————————— = ————————
91 91
Equation at the end of step 4 :
91c - 81
———————— < 0
91
Step 5 :
5.1 Multiply both sides by 91
5.2 Divide both sides by 91
c-(81/91) < 0
Solve Basic Inequality :
5.3 Add 81/91 to both sides
c < 81/91
Inequality Plot :
5.4 Inequality plot for
c - 0.890 < 0
One solution was found :
c < 81/91How did we do?
Please leave us feedback.