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): "65.19" was replaced by "(6519/100)". 3 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 :
-(48/10)*q-((5/10)*q+(6519/100))<0
Step by step solution :
Step 1 :
6519
Simplify ————
100
Equation at the end of step 1 :
48 5 6519
(0-(——•q))-((——•q)+————) < 0
10 10 100
Step 2 :
1
Simplify —
2
Equation at the end of step 2 :
48 1 6519
(0-(——•q))-((—•q)+————) < 0
10 2 100
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| 5 | 0 | 2 | 2 |
| Product of all Prime Factors | 2 | 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 = 50
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. q • 50 —————————————————— = —————— L.C.M 100 R. Mult. • R. Num. 6519 —————————————————— = ———— 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:
q • 50 + 6519 50q + 6519
————————————— = ——————————
100 100
Equation at the end of step 3 :
48 (50q + 6519)
(0 - (—— • q)) - ———————————— < 0
10 100
Step 4 :
24
Simplify ——
5
Equation at the end of step 4 :
24 (50q + 6519)
(0 - (—— • q)) - ———————————— < 0
5 100
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 100
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 2 | 2 |
| 2 | 0 | 2 | 2 |
| Product of all Prime Factors | 5 | 100 | 100 |
Least Common Multiple:
100
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 = 20
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -24q • 20 —————————————————— = ————————— L.C.M 100 R. Mult. • R. Num. (50q+6519) —————————————————— = —————————— L.C.M 100
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
-24q • 20 - ((50q+6519)) -530q - 6519
———————————————————————— = ————————————
100 100
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-530q - 6519 = -53 • (10q + 123)
Equation at the end of step 6 :
-53 • (10q + 123)
————————————————— < 0
100
Step 7 :
7.1 Multiply both sides by 100
7.2 Divide both sides by -53
Remember to flip the inequality sign:
7.3 Divide both sides by 10
q+(123/10) > 0
Solve Basic Inequality :
7.4 Subtract 123/10 from both sides
q > -123/10
Inequality Plot :
7.5 Inequality plot for
-5.300 X - 65.190 > 0
One solution was found :
q > -123/10How did we do?
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