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): "0.9" was replaced by "(9/10)". 4 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 :
(35/100)*x-(48/10)-((52/10)-(9/10)*x)<0
Step by step solution :
Step 1 :
9
Simplify ——
10
Equation at the end of step 1 :
35 48 52 9
((———•x)-——)-(——-(——•x)) < 0
100 10 10 10
Step 2 :
26
Simplify ——
5
Equation at the end of step 2 :
35 48 26 9x
((———•x)-——)-(——-——) < 0
100 10 5 10
Step 3 :
Calculating the Least Common Multiple :
3.1 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 :
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 = 2
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. 26 • 2 —————————————————— = —————— L.C.M 10 R. Mult. • R. Num. 9x —————————————————— = —— 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:
26 • 2 - (9x) 52 - 9x
————————————— = ———————
10 10
Equation at the end of step 3 :
35 48 (52 - 9x)
((——— • x) - ——) - ————————— < 0
100 10 10
Step 4 :
24
Simplify ——
5
Equation at the end of step 4 :
35 24 (52 - 9x)
((——— • x) - ——) - ————————— < 0
100 5 10
Step 5 :
7
Simplify ——
20
Equation at the end of step 5 :
7 24 (52 - 9x)
((—— • x) - ——) - ————————— < 0
20 5 10
Step 6 :
Calculating the Least Common Multiple :
6.1 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 :
6.2 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 :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 7x —————————————————— = —— L.C.M 20 R. Mult. • R. Num. 24 • 4 —————————————————— = —————— L.C.M 20
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
7x - (24 • 4) 7x - 96
————————————— = ———————
20 20
Equation at the end of step 6 :
(7x - 96) (52 - 9x)
————————— - ————————— < 0
20 10
Step 7 :
Calculating the Least Common Multiple :
7.1 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 :
7.2 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 :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (7x-96) —————————————————— = ——————— L.C.M 20 R. Mult. • R. Num. (52-9x) • 2 —————————————————— = ——————————— L.C.M 20
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
(7x-96) - ((52-9x) • 2) 25x - 200
——————————————————————— = —————————
20 20
Step 8 :
Pulling out like terms :
8.1 Pull out like factors :
25x - 200 = 25 • (x - 8)
Equation at the end of step 8 :
25 • (x - 8)
———————————— < 0
20
Step 9 :
9.1 Multiply both sides by 20
9.2 Divide both sides by 25
Solve Basic Inequality :
9.3 Add 8 to both sides
x < 8
Inequality Plot :
9.4 Inequality plot for
1.250 X - 10.000 < 0
One solution was found :
x < 8How did we do?
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