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): "2.2" was replaced by "(22/10)". 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 :
(34/10)-(13/10)*y-((5/10)*y-(22/10))<0
Step by step solution :
Step 1 :
11
Simplify ——
5
Equation at the end of step 1 :
34 13 5 11
(——-(——•y))-((——•y)-——) < 0
10 10 10 5
Step 2 :
1
Simplify —
2
Equation at the end of step 2 :
34 13 1 11
(——-(——•y))-((—•y)-——) < 0
10 10 2 5
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 0 | 1 | 1 |
| Product of all Prime Factors | 2 | 5 | 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 = 5
Right_M = L.C.M / R_Deno = 2
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. y • 5 —————————————————— = ————— L.C.M 10 R. Mult. • R. Num. 11 • 2 —————————————————— = —————— 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:
y • 5 - (11 • 2) 5y - 22
———————————————— = ———————
10 10
Equation at the end of step 3 :
34 13 (5y - 22)
(—— - (—— • y)) - ————————— < 0
10 10 10
Step 4 :
13
Simplify ——
10
Equation at the end of step 4 :
34 13 (5y - 22)
(—— - (—— • y)) - ————————— < 0
10 10 10
Step 5 :
17
Simplify ——
5
Equation at the end of step 5 :
17 13y (5y - 22)
(—— - ———) - ————————— < 0
5 10 10
Step 6 :
Calculating the Least Common Multiple :
6.1 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 :
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 = 1
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 17 • 2 —————————————————— = —————— L.C.M 10 R. Mult. • R. Num. 13y —————————————————— = ——— L.C.M 10
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
17 • 2 - (13y) 34 - 13y
—————————————— = ————————
10 10
Equation at the end of step 6 :
(34 - 13y) (5y - 22)
—————————— - ————————— < 0
10 10
Step 7 :
Adding fractions which have a common denominator :
7.1 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:
(34-13y) - ((5y-22)) 56 - 18y
———————————————————— = ————————
10 10
Step 8 :
Pulling out like terms :
8.1 Pull out like factors :
56 - 18y = -2 • (9y - 28)
Equation at the end of step 8 :
-2 • (9y - 28)
—————————————— < 0
10
Step 9 :
9.1 Multiply both sides by 10
9.2 Divide both sides by -2
Remember to flip the inequality sign:
9.3 Divide both sides by 9
y-(28/9) > 0
Solve Basic Inequality :
9.4 Add 28/9 to both sides
y > 28/9
Inequality Plot :
9.5 Inequality plot for
-1.800 X + 5.600 > 0
One solution was found :
y > 28/9How did we do?
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