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): "1.2" was replaced by "(12/10)". 3 more similar replacement(s)
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater equal sign from both sides of the inequality :
-(36/10)-(-(3/10)*a+(12/10))≥0
Step by step solution :
Step 1 :
6
Simplify —
5
Equation at the end of step 1 :
36 3 6
(0-——)-((0-(——•a))+—) ≥ 0
10 10 5
Step 2 :
3
Simplify ——
10
Equation at the end of step 2 :
36 3 6
(0-——)-((0-(——•a))+—) ≥ 0
10 10 5
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 1 | 1 | 1 |
| Product of all Prime Factors | 10 | 5 | 10 |
Least Common Multiple:
10
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 = 1
Right_M = L.C.M / R_Deno = 2
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. -3a —————————————————— = ——— L.C.M 10 R. Mult. • R. Num. 6 • 2 —————————————————— = ————— L.C.M 10
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:
-3a + 6 • 2 12 - 3a
——————————— = ———————
10 10
Equation at the end of step 3 :
36 (12 - 3a)
(0 - ——) - ————————— ≥ 0
10 10
Step 4 :
18
Simplify ——
5
Equation at the end of step 4 :
18 (12 - 3a)
(0 - ——) - ————————— ≥ 0
5 10
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
12 - 3a = -3 • (a - 4)
Calculating the Least Common Multiple :
6.2 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 10
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 1 | 1 | 1 |
| 2 | 0 | 1 | 1 |
| Product of all Prime Factors | 5 | 10 | 10 |
Least Common Multiple:
10
Calculating Multipliers :
6.3 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 :
6.4 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -18 • 2 —————————————————— = ——————— L.C.M 10 R. Mult. • R. Num. -3 • (a-4) —————————————————— = —————————— L.C.M 10
Adding fractions that have a common denominator :
6.5 Adding up the two equivalent fractions
-18 • 2 - (-3 • (a-4)) 3a - 48
—————————————————————— = ———————
10 10
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
3a - 48 = 3 • (a - 16)
Equation at the end of step 7 :
3 • (a - 16)
———————————— ≥ 0
10
Step 8 :
8.1 Multiply both sides by 10
8.2 Divide both sides by 3
Solve Basic Inequality :
8.3 Add 16 to both sides
a ≥ 16
Inequality Plot :
8.4 Inequality plot for
0.300 X - 4.800 ≥ 0
One solution was found :
a ≥ 16How did we do?
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