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): "10.02" was replaced by "(1002/100)". 3 more similar replacement(s)
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater equal sign from both sides of the inequality :
a/(14/10)+(312/100)-((1002/100))≥0
Step by step solution :
Step 1 :
501
Simplify ———
50
Equation at the end of step 1 :
14 312 501
(—— + ———) - ——— ≥ 0
10 100 50
Step 2 :
78
Simplify ——
25
Equation at the end of step 2 :
14 78 501
(—— + ——) - ——— ≥ 0
10 25 50
Step 3 :
7
Simplify —
5
Equation at the end of step 3 :
7 78 501
(— + ——) - ——— ≥ 0
5 25 50
Step 4 :
7
Divide a by —
5
Equation at the end of step 4 :
5a 78 501
(—— + ——) - ——— ≥ 0
7 25 50
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 7
The right denominator is : 25
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 7 | 1 | 0 | 1 |
| 5 | 0 | 2 | 2 |
| Product of all Prime Factors | 7 | 25 | 175 |
Least Common Multiple:
175
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 = 25
Right_M = L.C.M / R_Deno = 7
Making Equivalent Fractions :
5.3 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. 5a • 25 —————————————————— = ——————— L.C.M 175 R. Mult. • R. Num. 78 • 7 —————————————————— = —————— L.C.M 175
Adding fractions that have a common denominator :
5.4 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:
5a • 25 + 78 • 7 125a + 546
———————————————— = ——————————
175 175
Equation at the end of step 5 :
(125a + 546) 501
———————————— - ——— ≥ 0
175 50
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 175
The right denominator is : 50
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 2 | 2 | 2 |
| 7 | 1 | 0 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 175 | 50 | 350 |
Least Common Multiple:
350
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 = 2
Right_M = L.C.M / R_Deno = 7
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (125a+546) • 2 —————————————————— = —————————————— L.C.M 350 R. Mult. • R. Num. 501 • 7 —————————————————— = ——————— L.C.M 350
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
(125a+546) • 2 - (501 • 7) 250a - 2415
—————————————————————————— = ———————————
350 350
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
250a - 2415 = 5 • (50a - 483)
Equation at the end of step 7 :
5 • (50a - 483)
——————————————— ≥ 0
350
Step 8 :
8.1 Multiply both sides by 350
8.2 Divide both sides by 5
8.3 Divide both sides by 50
a-(483/50) ≥ 0
Solve Basic Inequality :
8.4 Add 483/50 to both sides
a ≥ 483/50
Inequality Plot :
8.5 Inequality plot for
0.714 X - 6.900 ≥ 0
One solution was found :
a ≥ 483/50How did we do?
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