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): "8.7" was replaced by "(87/10)". 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 :
-(92/10)*m-((385/100)-(87/10)*m)<0
Step by step solution :
Step 1 :
87
Simplify ——
10
Equation at the end of step 1 :
92 385 87
(0-(——•m))-(———-(——•m)) < 0
10 100 10
Step 2 :
77
Simplify ——
20
Equation at the end of step 2 :
92 77 87m
(0 - (—— • m)) - (—— - ———) < 0
10 20 10
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 20
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 20 | 10 | 20 |
Least Common Multiple:
20
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. 77 —————————————————— = —— L.C.M 20 R. Mult. • R. Num. 87m • 2 —————————————————— = ——————— L.C.M 20
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:
77 - (87m • 2) 77 - 174m
—————————————— = —————————
20 20
Equation at the end of step 3 :
92 (77 - 174m)
(0 - (—— • m)) - ——————————— < 0
10 20
Step 4 :
46
Simplify ——
5
Equation at the end of step 4 :
46 (77 - 174m)
(0 - (—— • m)) - ——————————— < 0
5 20
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 20
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 1 | 1 |
| 2 | 0 | 2 | 2 |
| Product of all Prime Factors | 5 | 20 | 20 |
Least Common Multiple:
20
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 = 4
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -46m • 4 —————————————————— = ———————— L.C.M 20 R. Mult. • R. Num. (77-174m) —————————————————— = ————————— L.C.M 20
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
-46m • 4 - ((77-174m)) -10m - 77
—————————————————————— = —————————
20 20
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-10m - 77 = -1 • (10m + 77)
Equation at the end of step 6 :
-10m - 77
————————— < 0
20
Step 7 :
7.1 Multiply both sides by 20
7.2 Multiply both sides by (-1)
Flip the inequality sign since you are multiplying by a negative number
10m+77 > 0
7.3 Divide both sides by 10
m+(77/10) > 0
Solve Basic Inequality :
7.4 Subtract 77/10 from both sides
m > -77/10
Inequality Plot :
7.5 Inequality plot for
-0.500 m - 3.850 < 0
One solution was found :
m > -77/10How did we do?
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