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How do you solve and check your solutions to $3.2 + \dfrac{x}{{2.5}} = 4.6$ ?

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Last updated date: 22nd Feb 2024
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IVSAT 2024
Answer
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Hint: First subtract the constant terms on both sides of the equation so that the $x$ variable gets isolated. Now in the next step multiply the entire equation with the decimal in the denominator of $x$ so that $x$ gets completely isolated. Now solve further to get the value of $x$ . Now to check if our answer, place the value back in the expression and solve. If we get LHS=RHS our answer is correct.

Complete step by step answer:
The given expression is $3.2 + \dfrac{x}{{2.5}} = 4.6$
Now firstly let’s subtract $3.2\;$ on both sides of the equation as a prime step to isolate the $x$ variable.
$ \Rightarrow 3.2 + \dfrac{x}{{2.5}} - 3.2 = 4.6 - 3.2$
Now evaluate the constants.
$ \Rightarrow \dfrac{x}{{2.5}} = 1.4$
Now multiply both the sides of the equation with $2.5\;$ to completely isolate the $x$ variable to get the solution easily.
$ \Rightarrow \dfrac{x}{{2.5}} \times 2.5 = 1.4 \times 2.5$
Now simplify further,
$ \Rightarrow x = 1.4 \times 2.5$
$ \Rightarrow x = 3.5$
Now since we got the value of $x$ , to check whether we got the correct answer or not, we substitute it back into the expression, $3.2 + \dfrac{x}{{2.5}} = 4.6$
$ \Rightarrow 3.2 + \dfrac{{3.5}}{{2.5}} = 4.6$
Since $3.5\;$ can be written as $\dfrac{{35}}{{10}}$ and also $2.5\;$ can be written as $\dfrac{{25}}{{10}}$
The denominators get cancelled and on further simplification evaluate the fraction and write it into decimal form.
$ \Rightarrow 3.2 + \dfrac{7}{5} = 4.6$
$ \Rightarrow 3.2 + 1.4 = 4.6$
Now on further simplifying we get,
$ \Rightarrow 4.6 = 4.6$
LHS=RHS. Hence proved that our answer is correct.

$\therefore $ The solution for the expression $3.2 + \dfrac{x}{{2.5}} = 4.6$ is $x = 3.5$

Note: Before converting a decimal into a fraction, always check the number of decimal places (number of digits) after the decimal place to convert the decimal into a fraction. The number of digits is then written to the power of $10\;$ and then placed in the denominator and in the numerator, the number will be written the same as it is , but without the decimal point.
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