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 less equal sign from both sides of the inequality :
(252/10)-(-(15/10)*y+(12/10))≤0
Step by step solution :
Step 1 :
6
Simplify —
5
Equation at the end of step 1 :
252 15 6
———-((0-(——•y))+—) ≤ 0
10 10 5
Step 2 :
3
Simplify —
2
Equation at the end of step 2 :
252 3 6
——— - ((0 - (— • y)) + —) ≤ 0
10 2 5
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 5
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 0 | 1 |
| 5 | 0 | 1 | 1 |
| Product of all Prime Factors | 2 | 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 = 5
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. -3y • 5 —————————————————— = ——————— 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:
-3y • 5 + 6 • 2 12 - 15y
——————————————— = ————————
10 10
Equation at the end of step 3 :
252 (12 - 15y)
——— - —————————— ≤ 0
10 10
Step 4 :
126
Simplify ———
5
Equation at the end of step 4 :
126 (12 - 15y)
——— - —————————— ≤ 0
5 10
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
12 - 15y = -3 • (5y - 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. 126 • 2 —————————————————— = ——————— L.C.M 10 R. Mult. • R. Num. -3 • (5y-4) —————————————————— = ——————————— L.C.M 10
Adding fractions that have a common denominator :
6.5 Adding up the two equivalent fractions
126 • 2 - (-3 • (5y-4)) 15y + 240
——————————————————————— = —————————
10 10
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
15y + 240 = 15 • (y + 16)
Equation at the end of step 7 :
15 • (y + 16)
————————————— ≤ 0
10
Step 8 :
8.1 Multiply both sides by 10
8.2 Divide both sides by 15
Solve Basic Inequality :
8.3 Subtract 16 from both sides
y ≤ -16
Inequality Plot :
8.4 Inequality plot for
1.500 X + 24.000 ≤ 0
One solution was found :
y ≤ -16How did we do?
Please leave us feedback.