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): "1.3" was replaced by "(13/10)". 3 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 :
(18/10)-((5/10)-(13/10)*p)<0
Step by step solution :
Step 1 :
13
Simplify ——
10
Equation at the end of step 1 :
18 5 13
—— - (—— - (—— • p)) < 0
10 10 10
Step 2 :
1
Simplify —
2
Equation at the end of step 2 :
18 1 13p
—— - (— - ———) < 0
10 2 10
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 1 | 1 |
| 5 | 0 | 1 | 1 |
| Product of all Prime Factors | 2 | 10 | 10 |
Least Common Multiple:
10
Calculating Multipliers :
3.2 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 = 5
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
3.3 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. 5 —————————————————— = —— L.C.M 10 R. Mult. • R. Num. 13p —————————————————— = ——— L.C.M 10
Adding fractions that have a common denominator :
3.4 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:
5 - (13p) 5 - 13p
————————— = ———————
10 10
Equation at the end of step 3 :
18 (5 - 13p)
—— - ————————— < 0
10 10
Step 4 :
9
Simplify —
5
Equation at the end of step 4 :
9 (5 - 13p)
— - ————————— < 0
5 10
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 1 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 5 | 10 | 10 |
Least Common Multiple:
10
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. 9 • 2 —————————————————— = ————— L.C.M 10 R. Mult. • R. Num. (5-13p) —————————————————— = ——————— L.C.M 10
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
9 • 2 - ((5-13p)) 13p + 13
————————————————— = ————————
10 10
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
13p + 13 = 13 • (p + 1)
Equation at the end of step 6 :
13 • (p + 1)
———————————— < 0
10
Step 7 :
7.1 Multiply both sides by 10
7.2 Divide both sides by 13
Solve Basic Inequality :
7.3 Subtract 1 from both sides
p < -1
Inequality Plot :
7.4 Inequality plot for
1.300 X + 1.300 < 0
One solution was found :
p < -1How did we do?
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