X:20=x:5 find x
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Answers
Answer:
X = 10
X = –10
Step by step explanation:
{ Step 1 }.
X/20 – ( 5/X )
{ Step 2 }.
simplify 5/x
equation at the end of step 2
x/20 – 5/x = 0
{ Step 2.1 }.
simplify x/20
equation at the end of step 2.1
x/20 – 5/x = 0
{ Step 3 }.
The least common multiple:
the left denominator is 20
the right denominator is x
[ process table given in attachment ⤴]
so, least common multiple = 20x
{ Step 3.1 }.
calculate multipliers for the two fractions:
Left M = LCM/L Deno. = x
Right M = LCM/R Deno. = 20
{ Step 3.2 }.
Making equation fraction:
To calculate equivalent fraction, multiply the numerator of each fraction by it's respective multiplier.
L multi. × L num. X × X
———————— = ————
L.C.M 20X
R multi. × R num. 5 × 20
————————— = ————
L.C.M 20X
{ Step 3.3 }
Adding fraction that have a common denominator:
X × X — ( 5 × 20 ) X² — 100
————————— = ——————
20X 20X
{ Step 3.4 }.
factor as a differences of square:
factoring x² – 100
= ( A² – B² )
check: 100 is the square of 10
check: x² is the square of x¹
factorization is
( x + 10 ) × ( x – 10 )
Equation at the end of step 3.
( X + 10 ) × ( X – 10)
—————————— = 0
20X
{ Step 4 }.
when a fraction equation zero:
( X + 10 ) × ( X – 10 )
—————————— × 20X = 0 × 20X
20X
( X + 10 ) × ( X – 10 ) = 0
{ Step 4.1 }.
Solving single variable equation:
(i). Solve, X + 10 = 0
=> X = – 10
(ii). Solve, X – 10 = 0
=> X = 10
➡Two solutions were found⬅
X = –10
X = 10
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