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How do you solve \[2x + 96(x + 12) = 180\]?

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Last updated date: 01st Mar 2024
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IVSAT 2024
Answer
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Hint: In the given problem we need to solve this for ‘x’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘x’ terms one side and constants on the other side of the equation.

Complete step by step solution:
Given, \[2x + 96(x + 12) = 180\].
Firstly we expand the brackets in left hand side of the equation,
\[2x + 96x + (96 \times 12) = 180\]
\[2x + 96x + 1152 = 180\]
We transpose ‘1152’ which is present in the left hand side of the equation to the right hand side of the equation by subtracting ‘1152’ on the right hand side of the equation.
\[2x + 96x = 180 - 1152\]
Simplifying we have
\[2x + 96x = - 972\]
Taking ‘x’ common we have,
\[x(2 + 96) = - 972\]
\[98x = - 972\]
We transpose 98 to the right side of the equation by dividing 98 on right hand side of the equation,
\[x = \dfrac{{ - 972}}{{98}}\]
\[x = \dfrac{{ - 486}}{{49}}\]
\[x = - 9.918\]
\[ \Rightarrow x = - 9.92\]. This is the required answer.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘x’ in the given problem.
\[2x + 96(x + 12) = 180\]
\[2 \times ( - 9.92) + 96 \times ( - 9.92 + 12) = 180\]
\[2 \times ( - 9.92) + 96 \times (2.08) = 180\]
\[ - 19.84 + 199.68 = 180\]
\[ \Rightarrow 179.84 = 180\].
Since we have decimal values in the obtained answer and the value is very close to 180. Hence the obtained answer is correct. Careful in the calculation part as it contains fractions.
In the above we did the transpose of addition and subtraction. Similarly if we have multiplication we use division to transpose. If we have division we use multiplication to transpose. Follow the same procedure for these kinds of problems.
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