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Solve the following equation \[\dfrac{{x - 1}}{2} - x + 13 = 5 - x\]

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Last updated date: 17th May 2024
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Answer
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Hint: Rearrange the given equation such that the unknown terms arranged on one side and all other terms are arranged on other side and then compare both sides and with further simplification we can determine the value of unknown terms.
Given: \[\dfrac{{x - 1}}{2} - x + 13 = 5 - x\]
To find: the value of ‘x’
Complete step by step answer:
Step 1: Firstly we will determine the number of unknown terms in the given equation.
\[\dfrac{{x - 1}}{2} - x + 13 = 5 - x\]
So here we have only one unknown term so we require only one equation to determine the value of ‘x’
Step 2: multiply both sides of the equation with 2 such that all the denominator part get reduced and we get a simple linear equation
\[\dfrac{{x - 1}}{2} - x + 13 = 5 - x\]
\[2 \times (\dfrac{{x - 1}}{2} - x + 13) = (5 - x) \times 2\]
Opening the bracket and we get
\[(x - 1) - 2 \times x + 2 \times 13 = 5 \times 2 - x \times 2\]
Step 3: rearranging the terms such that the unknown term arranged on one side and all other terms are arranged on other side, that is
\[(x - 1) - 2 \times x + 2 \times 13 = 5 \times 2 - x \times 2\]
\[x - 2x - 1 + 26 = 10 - 2x\]
\[x - 2x + 2x = 10 + 1 - 26\]
On further simplification, we get
\[x - 2x + 2x = 10 + 1 - 26\]
\[x = - 15\]
Hence, on solving the given equation we determined the value of ‘x’ and it is equal to \[x = - 15\]

Note: We have different solution methods for different types of equation
We can use the substitution method
We can use the elimination method without multiplication.
We can use the elimination method with multiplication.
There might be the possibility of infinite solution or no solution.