Key to "54x+3=14+14x"

Brittney Lord

Answered question

2021-09-15

\frac{5}{4} x + 3 = \frac{1}{4} + \frac{1}{4} x

Answer & Explanation

Luvottoq

Skilled2021-09-16Added 95 answers

Step 1
Given,
The equation is,

\frac{5}{4} x + 3 = \frac{1}{4} + \frac{1}{4} x

Step 2
The given equation can be rewrite as,

\frac{5}{4} x + \frac{3}{1} = \frac{1}{4} + \frac{1}{4} x

This is an rational equation.
So to solve this equation first find the least common denominator (LCD),
The least common denominator (LCD) is the smallest number that can be a common denominator for a fractions.
So for the least common denominator (LCD) find the least common multiple of the denominators 4, 1,4,4.
Thus the least common denominator (LCD) is 4.
Multiply by LCD 4 to the both side of the equation,

\Rightarrow 5 x + 12 = 1 + x

Subtracting 12 from both sides,

\Rightarrow 5 x + 12 - 12 = 1 + x - 12

\Rightarrow 5 x = - 11 + x

Subtracting x from both sides,

\Rightarrow 5 x - x = - 11 + x - x

\Rightarrow 4 x = - 11

Dividing by 4 to the both sides,

\Rightarrow x = \frac{- 11}{4}

\Rightarrow x = - 2.75

Thus the solution of the given equation is

x = - 2.75

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