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): "6.6" was replaced by "(66/10)". 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 :
-(245/100)*x+(32/10)-(-(66/10))<0
Step by step solution :
Step 1 :
33
Simplify ——
5
Equation at the end of step 1 :
245 32 33
((0-(———•x))+——)-(0-——) < 0
100 10 5
Step 2 :
16
Simplify ——
5
Equation at the end of step 2 :
245 16 -33
((0 - (——— • x)) + ——) - ——— < 0
100 5 5
Step 3 :
49
Simplify ——
20
Equation at the end of step 3 :
49 16 -33
((0 - (—— • x)) + ——) - ——— < 0
20 5 5
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 20
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 0 | 2 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 20 | 5 | 20 |
Least Common Multiple:
20
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 = 1
Right_M = L.C.M / R_Deno = 4
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. -49x —————————————————— = ———— L.C.M 20 R. Mult. • R. Num. 16 • 4 —————————————————— = —————— L.C.M 20
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:
-49x + 16 • 4 64 - 49x
————————————— = ————————
20 20
Equation at the end of step 4 :
(64 - 49x) -33
—————————— - ——— < 0
20 5
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 20
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 0 | 2 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 20 | 5 | 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 = 1
Right_M = L.C.M / R_Deno = 4
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (64-49x) —————————————————— = ———————— L.C.M 20 R. Mult. • R. Num. -33 • 4 —————————————————— = ——————— L.C.M 20
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(64-49x) - (-33 • 4) 196 - 49x
———————————————————— = —————————
20 20
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
196 - 49x = -49 • (x - 4)
Equation at the end of step 6 :
-49 • (x - 4)
————————————— < 0
20
Step 7 :
7.1 Multiply both sides by 20
7.2 Divide both sides by -49
Remember to flip the inequality sign:
Solve Basic Inequality :
7.3 Add 4 to both sides
x > 4
Inequality Plot :
7.4 Inequality plot for
-2.450 X + 9.800 > 0
One solution was found :
x > 4How did we do?
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