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 less equal sign from both sides of the inequality :
5-x/4-(1/2)≤0
Step by step solution :
Step 1 :
1
Simplify —
2
Equation at the end of step 1 :
x 1
(5 - —) - — ≤ 0
4 2
Step 2 :
x
Simplify —
4
Equation at the end of step 2 :
x 1
(5 - —) - — ≤ 0
4 2
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 4 as the denominator :
5 5 • 4
5 = — = —————
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 :
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:
5 • 4 - (x) 20 - x
——————————— = ——————
4 4
Equation at the end of step 3 :
(20 - x) 1
———————— - — ≤ 0
4 2
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 4
The right denominator is : 2
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 1 | 2 |
| Product of all Prime Factors | 4 | 2 | 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 = 1
Right_M = L.C.M / R_Deno = 2
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. (20-x) —————————————————— = —————— L.C.M 4 R. Mult. • R. Num. 2 —————————————————— = — L.C.M 4
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
(20-x) - (2) 18 - x
———————————— = ——————
4 4
Equation at the end of step 4 :
18 - x
—————— ≤ 0
4
Step 5 :
5.1 Multiply both sides by 4
5.2 Multiply both sides by (-1)
Flip the inequality sign since you are multiplying by a negative number
x-18 ≥ 0
Solve Basic Inequality :
5.3 Add 18 to both sides
x ≥ 18
Inequality Plot :
5.4 Inequality plot for
-0.250 x + 4.500 ≤ 0
One solution was found :
x ≥ 18How did we do?
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