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 :
5/3*p-25/6*p-(15/4)<0
Step by step solution :
Step 1 :
15
Simplify ——
4
Equation at the end of step 1 :
5 25 15
((—•p)-(——•p))-—— < 0
3 6 4
Step 2 :
25
Simplify ——
6
Equation at the end of step 2 :
5 25 15
((— • p) - (—— • p)) - —— < 0
3 6 4
Step 3 :
5
Simplify —
3
Equation at the end of step 3 :
5 25p 15
((— • p) - ———) - —— < 0
3 6 4
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 6
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 1 | 1 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 3 | 6 | 6 |
Least Common Multiple:
6
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. 5p • 2 —————————————————— = —————— L.C.M 6 R. Mult. • R. Num. 25p —————————————————— = ——— L.C.M 6
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:
5p • 2 - (25p) -15p
—————————————— = ————
6 6
Equation at the end of step 4 :
-15p 15
———— - —— < 0
6 4
Step 5 :
Calculating the Least Common Multiple :
5.1 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 :
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 = 2
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -5p • 2 —————————————————— = ——————— L.C.M 4 R. Mult. • R. Num. 15 —————————————————— = —— L.C.M 4
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
-5p • 2 - (15) -10p - 15
—————————————— = —————————
4 4
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-10p - 15 = -5 • (2p + 3)
Equation at the end of step 6 :
-5 • (2p + 3)
————————————— < 0
4
Step 7 :
7.1 Multiply both sides by 4
7.2 Divide both sides by -5
Remember to flip the inequality sign:
7.3 Divide both sides by 2
p+(3/2) > 0
Solve Basic Inequality :
7.4 Subtract 3/2 from both sides
p > -3/2
Inequality Plot :
7.5 Inequality plot for
-2.500 X - 3.750 > 0
One solution was found :
p > -3/2How did we do?
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