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): "2.4" was replaced by "(24/10)". 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 :
-(42/10)-(11/10)*m-((24/10))<0
Step by step solution :
Step 1 :
12
Simplify ——
5
Equation at the end of step 1 :
42 11 12
((0-——)-(——•m))-—— < 0
10 10 5
Step 2 :
11
Simplify ——
10
Equation at the end of step 2 :
42 11 12
((0 - ——) - (—— • m)) - —— < 0
10 10 5
Step 3 :
21
Simplify ——
5
Equation at the end of step 3 :
21 11m 12
((0 - ——) - ———) - —— < 0
5 10 5
Step 4 :
Calculating the Least Common Multiple :
4.1 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 :
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. -21 • 2 —————————————————— = ——————— L.C.M 10 R. Mult. • R. Num. 11m —————————————————— = ——— L.C.M 10
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:
-21 • 2 - (11m) -11m - 42
——————————————— = —————————
10 10
Equation at the end of step 4 :
(-11m - 42) 12
——————————— - —— < 0
10 5
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-11m - 42 = -1 • (11m + 42)
Calculating the Least Common Multiple :
6.2 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 :
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 = 2
Making Equivalent Fractions :
6.4 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (-11m-42) —————————————————— = ————————— L.C.M 10 R. Mult. • R. Num. 12 • 2 —————————————————— = —————— L.C.M 10
Adding fractions that have a common denominator :
6.5 Adding up the two equivalent fractions
(-11m-42) - (12 • 2) -11m - 66
———————————————————— = —————————
10 10
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
-11m - 66 = -11 • (m + 6)
Equation at the end of step 7 :
-11 • (m + 6)
————————————— < 0
10
Step 8 :
8.1 Multiply both sides by 10
8.2 Divide both sides by -11
Remember to flip the inequality sign:
Solve Basic Inequality :
8.3 Subtract 6 from both sides
m > -6
Inequality Plot :
8.4 Inequality plot for
-1.100 X - 6.600 > 0
One solution was found :
m > -6How did we do?
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