Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
3/16*x+58/100-(13/10)>0
Step by step solution :
Step 1 :
13
Simplify ——
10
Equation at the end of step 1 :
3 58 13
((—— • x) + ———) - —— > 0
16 100 10
Step 2 :
29
Simplify ——
50
Equation at the end of step 2 :
3 29 13
((—— • x) + ——) - —— > 0
16 50 10
Step 3 :
3
Simplify ——
16
Equation at the end of step 3 :
3 29 13
((—— • x) + ——) - —— > 0
16 50 10
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 16
The right denominator is : 50
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 4 | 1 | 4 |
| 5 | 0 | 2 | 2 |
| Product of all Prime Factors | 16 | 50 | 400 |
Least Common Multiple:
400
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 = 25
Right_M = L.C.M / R_Deno = 8
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. 3x • 25 —————————————————— = ——————— L.C.M 400 R. Mult. • R. Num. 29 • 8 —————————————————— = —————— L.C.M 400
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:
3x • 25 + 29 • 8 75x + 232
———————————————— = —————————
400 400
Equation at the end of step 4 :
(75x + 232) 13
——————————— - —— > 0
400 10
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 400
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 4 | 1 | 4 |
| 5 | 2 | 1 | 2 |
| Product of all Prime Factors | 400 | 10 | 400 |
Least Common Multiple:
400
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 = 40
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (75x+232) —————————————————— = ————————— L.C.M 400 R. Mult. • R. Num. 13 • 40 —————————————————— = ——————— L.C.M 400
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(75x+232) - (13 • 40) 75x - 288
————————————————————— = —————————
400 400
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
75x - 288 = 3 • (25x - 96)
Equation at the end of step 6 :
3 • (25x - 96)
—————————————— > 0
400
Step 7 :
7.1 Multiply both sides by 400
7.2 Divide both sides by 3
7.3 Divide both sides by 25
x-(96/25) > 0
Solve Basic Inequality :
7.4 Add 96/25 to both sides
x > 96/25
Inequality Plot :
7.5 Inequality plot for
0.188 X - 0.720 > 0
One solution was found :
x > 96/25How did we do?
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