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 :
5-3/8*d-(10/14)<0
Step by step solution :
Step 1 :
5
Simplify —
7
Equation at the end of step 1 :
3 5
(5 - (— • d)) - — < 0
8 7
Step 2 :
3
Simplify —
8
Equation at the end of step 2 :
3 5
(5 - (— • d)) - — < 0
8 7
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 8 as the denominator :
5 5 • 8
5 = — = —————
1 8
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 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:
5 • 8 - (3d) 40 - 3d
———————————— = ———————
8 8
Equation at the end of step 3 :
(40 - 3d) 5
————————— - — < 0
8 7
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 8
The right denominator is : 7
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 3 | 0 | 3 |
| 7 | 0 | 1 | 1 |
| Product of all Prime Factors | 8 | 7 | 56 |
Least Common Multiple:
56
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 = 7
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. (40-3d) • 7 —————————————————— = ——————————— L.C.M 56 R. Mult. • R. Num. 5 • 8 —————————————————— = ————— L.C.M 56
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
(40-3d) • 7 - (5 • 8) 240 - 21d
————————————————————— = —————————
56 56
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
240 - 21d = -3 • (7d - 80)
Equation at the end of step 5 :
-3 • (7d - 80)
—————————————— < 0
56
Step 6 :
6.1 Multiply both sides by 56
6.2 Divide both sides by -3
Remember to flip the inequality sign:
6.3 Divide both sides by 7
d-(80/7) > 0
Solve Basic Inequality :
6.4 Add 80/7 to both sides
d > 80/7
Inequality Plot :
6.5 Inequality plot for
-0.375 X + 4.286 > 0
One solution was found :
d > 80/7How did we do?
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