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): "10." was replaced by "(10/1)". 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 :
(25/10)*x+(325/100)*x+(10/1)-(20)≤0
Step by step solution :
Step 1 :
10
Simplify ——
1
Equation at the end of step 1 :
25 325
(((——•x)+(———•x))+10)-20 ≤ 0
10 100
Step 2 :
13
Simplify ——
4
Equation at the end of step 2 :
25 13
(((——•x)+(——•x))+10)-20 ≤ 0
10 4
Step 3 :
5
Simplify —
2
Equation at the end of step 3 :
5 13x
(((— • x) + ———) + 10) - 20 ≤ 0
2 4
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 4
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 1 | 2 | 2 |
| Product of all Prime Factors | 2 | 4 | 4 |
Least Common Multiple:
4
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. 5x • 2 —————————————————— = —————— L.C.M 4 R. Mult. • R. Num. 13x —————————————————— = ——— L.C.M 4
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:
5x • 2 + 13x 23x
———————————— = ———
4 4
Equation at the end of step 4 :
23x
(——— + 10) - 20 ≤ 0
4
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 4 as the denominator :
10 10 • 4
10 = —— = ——————
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 :
5.2 Adding up the two equivalent fractions
23x + 10 • 4 23x + 40
———————————— = ————————
4 4
Equation at the end of step 5 :
(23x + 40)
—————————— - 20 ≤ 0
4
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 4 as the denominator :
20 20 • 4
20 = —— = ——————
1 4
Adding fractions that have a common denominator :
6.2 Adding up the two equivalent fractions
(23x+40) - (20 • 4) 23x - 40
——————————————————— = ————————
4 4
Equation at the end of step 6 :
23x - 40
———————— ≤ 0
4
Step 7 :
7.1 Multiply both sides by 4
7.2 Divide both sides by 23
x-(40/23) ≤ 0
Solve Basic Inequality :
7.3 Add 40/23 to both sides
x ≤ 40/23
Inequality Plot :
7.4 Inequality plot for
5.750 x - 10.000 ≤ 0
One solution was found :
x ≤ 40/23How did we do?
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