Reformatting the input :
Changes made to your input should not affect the solution:
(1): "48.07" was replaced by "(4807/100)". 5 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 :
-8*(-(252/10)*x-(2376/100))-(974/10)*x-(-4*(-(233/10)*x-(4807/100)))>0
Step by step solution :
Step 1 :
4807 Simplify ———— 100 Equation at the end of step 1 :
252 2376 974 233 4807 ((0-(8•((0-(———•x))-————)))-(———•x))-(0-(4•((0-(———•x))-————))) > 0 10 100 10 10 100 Step 2 :
233 Simplify ——— 10 Equation at the end of step 2 :
252 2376 974 233 4807 ((0-(8•((0-(———•x))-————)))-(———•x))-(0-(4•((0-(———•x))-————))) > 0 10 100 10 10 100 Step 3 :
Calculating the Least Common Multiple :
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| 5 | 1 | 2 | 2 |
| Product of all Prime Factors | 10 | 100 | 100 |
Least Common Multiple:
100
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=10
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. -233x • 10 —————————————————— = —————————— L.C.M 100 R. Mult. • R. Num. 4807 —————————————————— = ———— L.C.M 100
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:
-233x • 10 - (4807) -2330x - 4807 ——————————————————— = ————————————— 100 100 Equation at the end of step 3 :
252 2376 974 (-2330x-4807) ((0-(8•((0-(———•x))-————)))-(———•x))-(0-(4•—————————————)) > 0 10 100 10 100 Step 4 :
Step 5 :
Pulling out like terms :
5.1 Pull out like factors:
-2330x - 4807=-1•(2330x + 4807)
Equation at the end of step 5 :
252 2376 974 (-2330x-4807) ((0-(8•((0-(———•x))-————)))-(———•x))-(0-—————————————) > 0 10 100 10 25 Step 6 :
487 Simplify ——— 5 Equation at the end of step 6 :
252 2376 487 (2330x+4807) ((0-(8•((0-(———•x))-————)))-(———•x))-———————————— > 0 10 100 5 25 Step 7 :
594 Simplify ——— 25 Equation at the end of step 7 :
252 594 487x (2330x+4807) ((0-(8•((0-(———•x))-———)))-————)-———————————— > 0 10 25 5 25 Step 8 :
126 Simplify ——— 5 Equation at the end of step 8 :
126 594 487x (2330x+4807) ((0-(8•((0-(———•x))-———)))-————)-———————————— > 0 5 25 5 25 Step 9 :
Calculating the Least Common Multiple :
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 2 | 2 |
| Product of all Prime Factors | 5 | 25 | 25 |
Least Common Multiple:
25
Calculating Multipliers :
9.2 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 :
9.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -126x • 5 —————————————————— = ————————— L.C.M 25 R. Mult. • R. Num. 594 —————————————————— = ——— L.C.M 25
Adding fractions that have a common denominator :
9.4 Adding up the two equivalent fractions
-126x • 5 - (594) -630x - 594 ————————————————— = ——————————— 25 25 Equation at the end of step 9 :
(-630x - 594) 487x (2330x + 4807) ((0 - (8 • —————————————)) - ————) - —————————————— > 0 25 5 25 Step 10 :
Step 11 :
Pulling out like terms :
11.1 Pull out like factors:
-630x - 594=-18•(35x + 33)
Equation at the end of step 11 :
-144 • (35x + 33) 487x (2330x + 4807) ((0 - —————————————————) - ————) - —————————————— > 0 25 5 25 Step 12 :
Calculating the Least Common Multiple :
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 25 | 5 | 25 |
Least Common Multiple:
25
Calculating Multipliers :
12.2 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=5
Making Equivalent Fractions :
12.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 144 • (35x+33) —————————————————— = —————————————— L.C.M 25 R. Mult. • R. Num. 487x • 5 —————————————————— = ———————— L.C.M 25
Adding fractions that have a common denominator :
12.4 Adding up the two equivalent fractions
144 • (35x+33) - (487x • 5) 2605x + 4752 ——————————————————————————— = ———————————— 25 25 Equation at the end of step 12 :
(2605x + 4752) (2330x + 4807) —————————————— - —————————————— > 0 25 25 Step 13 :
Adding fractions which have a common denominator :
13.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(2605x+4752) - ((2330x+4807)) 275x - 55 ————————————————————————————— = ————————— 25 25 Step 14 :
Pulling out like terms :
14.1 Pull out like factors:
275x - 55=55•(5x - 1)
Equation at the end of step 14 :
55 • (5x - 1) ————————————— > 0 25 Step 15 :
Solve Basic Inequality :
15.4 Add 1/5 to both sidesx > 1/5
Inequality Plot :
15.5 Inequality plot for11.000 X - 2.200 > 0
One solution was found :
x > 1/5
