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 :
-4/3*x+1/6-(7/9)<0
Step by step solution :
Step 1 :
7
Simplify —
9
Equation at the end of step 1 :
4 1 7
((0-(—•x))+—)-— < 0
3 6 9
Step 2 :
1
Simplify —
6
Equation at the end of step 2 :
4 1 7
((0 - (— • x)) + —) - — < 0
3 6 9
Step 3 :
4
Simplify —
3
Equation at the end of step 3 :
4 1 7
((0 - (— • x)) + —) - — < 0
3 6 9
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 6
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 1 | 1 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 3 | 6 | 6 |
Least Common Multiple:
6
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 = 2
Right_M = L.C.M / R_Deno = 1
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. -4x • 2 —————————————————— = ——————— L.C.M 6 R. Mult. • R. Num. 1 —————————————————— = — L.C.M 6
Adding fractions that have a common denominator :
4.4 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:
-4x • 2 + 1 1 - 8x
——————————— = ——————
6 6
Equation at the end of step 4 :
(1 - 8x) 7
———————— - — < 0
6 9
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 6
The right denominator is : 9
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 3 | 1 | 2 | 2 |
| Product of all Prime Factors | 6 | 9 | 18 |
Least Common Multiple:
18
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 = 3
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (1-8x) • 3 —————————————————— = —————————— L.C.M 18 R. Mult. • R. Num. 7 • 2 —————————————————— = ————— L.C.M 18
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(1-8x) • 3 - (7 • 2) -24x - 11
———————————————————— = —————————
18 18
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-24x - 11 = -1 • (24x + 11)
Equation at the end of step 6 :
-24x - 11
————————— < 0
18
Step 7 :
7.1 Multiply both sides by 18
7.2 Multiply both sides by (-1)
Flip the inequality sign since you are multiplying by a negative number
24x+11 > 0
7.3 Divide both sides by 24
x+(11/24) > 0
Solve Basic Inequality :
7.4 Subtract 11/24 from both sides
x > -11/24
Inequality Plot :
7.5 Inequality plot for
-1.333 x - 0.611 < 0
One solution was found :
x > -11/24How did we do?
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