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 :
x/3-x-1/2-(2)<0
Step by step solution :
Step 1 :
1
Simplify —
2
Equation at the end of step 1 :
x 1
((— - x) - —) - 2 < 0
3 2
Step 2 :
x
Simplify —
3
Equation at the end of step 2 :
x 1
((— - x) - —) - 2 < 0
3 2
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
x x • 3
x = — = —————
1 3
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:
x - (x • 3) -2x
——————————— = ———
3 3
Equation at the end of step 3 :
-2x 1
(——— - —) - 2 < 0
3 2
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 2
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 1 | 0 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 3 | 2 | 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 = 3
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. -2x • 2 —————————————————— = ——————— L.C.M 6 R. Mult. • R. Num. 3 —————————————————— = — L.C.M 6
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
-2x • 2 - (3) -4x - 3
————————————— = ———————
6 6
Equation at the end of step 4 :
(-4x - 3)
————————— - 2 < 0
6
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 6 as the denominator :
2 2 • 6
2 = — = —————
1 6
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-4x - 3 = -1 • (4x + 3)
Adding fractions that have a common denominator :
6.2 Adding up the two equivalent fractions
(-4x-3) - (2 • 6) -4x - 15
————————————————— = ————————
6 6
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
-4x - 15 = -1 • (4x + 15)
Equation at the end of step 7 :
-4x - 15
———————— < 0
6
Step 8 :
8.1 Multiply both sides by 6
8.2 Multiply both sides by (-1)
Flip the inequality sign since you are multiplying by a negative number
4x+15 > 0
8.3 Divide both sides by 4
x+(15/4) > 0
Solve Basic Inequality :
8.4 Subtract 15/4 from both sides
x > -15/4
Inequality Plot :
8.5 Inequality plot for
-0.667 x - 2.500 < 0
One solution was found :
x > -15/4How did we do?
Please leave us feedback.