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 :
7/4-3*x-(5/6)<0
Step by step solution :
Step 1 :
5
Simplify —
6
Equation at the end of step 1 :
7 5
(— - 3x) - — < 0
4 6
Step 2 :
7
Simplify —
4
Equation at the end of step 2 :
7 5
(— - 3x) - — < 0
4 6
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 4 as the denominator :
3x 3x • 4
3x = —— = ——————
1 4
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:
7 - (3x • 4) 7 - 12x
———————————— = ———————
4 4
Equation at the end of step 3 :
(7 - 12x) 5
————————— - — < 0
4 6
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 4
The right denominator is : 6
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| 3 | 0 | 1 | 1 |
| Product of all Prime Factors | 4 | 6 | 12 |
Least Common Multiple:
12
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 = 3
Right_M = L.C.M / R_Deno = 2
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. (7-12x) • 3 —————————————————— = ——————————— L.C.M 12 R. Mult. • R. Num. 5 • 2 —————————————————— = ————— L.C.M 12
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
(7-12x) • 3 - (5 • 2) 11 - 36x
————————————————————— = ————————
12 12
Equation at the end of step 4 :
11 - 36x
———————— < 0
12
Step 5 :
5.1 Multiply both sides by 12
5.2 Multiply both sides by (-1)
Flip the inequality sign since you are multiplying by a negative number
36x-11 > 0
5.3 Divide both sides by 36
x-(11/36) > 0
Solve Basic Inequality :
5.4 Add 11/36 to both sides
x > 11/36
Inequality Plot :
5.5 Inequality plot for
-3.000 x + 0.917 < 0
One solution was found :
x > 11/36How did we do?
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