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 :
4*g-2/5-(1/3)<0
Step by step solution :
Step 1 :
1
Simplify —
3
Equation at the end of step 1 :
2 1
(4g - —) - — < 0
5 3
Step 2 :
2
Simplify —
5
Equation at the end of step 2 :
2 1
(4g - —) - — < 0
5 3
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 5 as the denominator :
4g 4g • 5
4g = —— = ——————
1 5
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:
4g • 5 - (2) 20g - 2
———————————— = ———————
5 5
Equation at the end of step 3 :
(20g - 2) 1
————————— - — < 0
5 3
Step 4 :
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
20g - 2 = 2 • (10g - 1)
Calculating the Least Common Multiple :
5.2 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 3
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 0 | 1 |
| 3 | 0 | 1 | 1 |
| Product of all Prime Factors | 5 | 3 | 15 |
Least Common Multiple:
15
Calculating Multipliers :
5.3 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 = 3
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
5.4 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. 2 • (10g-1) • 3 —————————————————— = ——————————————— L.C.M 15 R. Mult. • R. Num. 5 —————————————————— = —— L.C.M 15
Adding fractions that have a common denominator :
5.5 Adding up the two equivalent fractions
2 • (10g-1) • 3 - (5) 60g - 11
————————————————————— = ————————
15 15
Equation at the end of step 5 :
60g - 11
———————— < 0
15
Step 6 :
6.1 Multiply both sides by 15
6.2 Divide both sides by 60
g-(11/60) < 0
Solve Basic Inequality :
6.3 Add 11/60 to both sides
g < 11/60
Inequality Plot :
6.4 Inequality plot for
4.000 g - 0.733 < 0
One solution was found :
g < 11/60How did we do?
Please leave us feedback.