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): "1.4" was replaced by "(14/10)". 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 :
-(439/100)-(-(23/10)*n-(14/10))<0
Step by step solution :
Step 1 :
7
Simplify —
5
Equation at the end of step 1 :
439 23 7
(0-———)-((0-(——•n))-—) < 0
100 10 5
Step 2 :
23
Simplify ——
10
Equation at the end of step 2 :
439 23 7
(0-———)-((0-(——•n))-—) < 0
100 10 5
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 10 | 5 | 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 = 1
Right_M = L.C.M / R_Deno = 2
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. -23n —————————————————— = ———— L.C.M 10 R. Mult. • R. Num. 7 • 2 —————————————————— = ————— 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:
-23n - (7 • 2) -23n - 14
—————————————— = —————————
10 10
Equation at the end of step 3 :
439 (-23n - 14)
(0 - ———) - ——————————— < 0
100 10
Step 4 :
439
Simplify ———
100
Equation at the end of step 4 :
439 (-23n - 14)
(0 - ———) - ——————————— < 0
100 10
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-23n - 14 = -1 • (23n + 14)
Calculating the Least Common Multiple :
6.2 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 100 | 10 | 100 |
Least Common Multiple:
100
Calculating Multipliers :
6.3 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 = 1
Right_M = L.C.M / R_Deno = 10
Making Equivalent Fractions :
6.4 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -439 —————————————————— = ———— L.C.M 100 R. Mult. • R. Num. (-23n-14) • 10 —————————————————— = —————————————— L.C.M 100
Adding fractions that have a common denominator :
6.5 Adding up the two equivalent fractions
-439 - ((-23n-14) • 10) 230n - 299
——————————————————————— = ——————————
100 100
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
230n - 299 = 23 • (10n - 13)
Equation at the end of step 7 :
23 • (10n - 13)
——————————————— < 0
100
Step 8 :
8.1 Multiply both sides by 100
8.2 Divide both sides by 23
8.3 Divide both sides by 10
n-(13/10) < 0
Solve Basic Inequality :
8.4 Add 13/10 to both sides
n < 13/10
Inequality Plot :
8.5 Inequality plot for
2.300 X - 2.990 < 0
One solution was found :
n < 13/10How did we do?
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