Questions & Answers

Question

Answers

A) $12$

B) $6$

C) $3$

D) $15$

Answer
Verified

Hint: The given problem is related to a linear equation in one variable. To solve this problem, take all the terms containing the variable to the left-hand side of the equation and remaining terms to the right-hand side of the equation. Then solve the equation to find the value of the variable.

Complete step-by-step answer:

Letâ€™s consider the linear equation in one variable given by $ax+b=c$, where $a, b$ and $c$ are constants and $x$ is the variable. On a cartesian plane, this equation represents a straight line parallel to the $y$ axis. To find the value of the variable, we will take all the terms containing the variable to the left-hand side of the equation and remaining terms to the right-hand side of the equation. So, we get:

$ax=c-b$ . Finally, the value of the variable $x$ is given by $x=\dfrac{c-b}{a}$.

For example: Consider the equation $x+9=13$ and compare with $ax+b=c$, we get:

$a=1, b=9$ and $c=13$.

Now, to find the value of the variable $x$, we will take all the terms containing the variable to the left-hand side of the equation and remaining terms to the right-hand side of the equation. So, we get

$x=13-9=4$. Hence, $x=4$ is the solution.

Now, coming to the given question, we are given $p+3=9$. To find the value of the variable $p$, we will take all the terms containing the variable to the left-hand side of the equation and remaining terms to the right-hand side of the equation. So, we get

$p=9-3=6$ . Hence, $p=6$ is the solution.

Hence, option B. is the correct answer.

Note: While shifting the constants from left-hand side of the equation to the right-hand side of the equation, do not forget to change the sign of the constant, i.e. if the sign is positive, change it to negative and vice-versa. Students generally forget to change the sign and end up getting a wrong answer.

Complete step-by-step answer:

Letâ€™s consider the linear equation in one variable given by $ax+b=c$, where $a, b$ and $c$ are constants and $x$ is the variable. On a cartesian plane, this equation represents a straight line parallel to the $y$ axis. To find the value of the variable, we will take all the terms containing the variable to the left-hand side of the equation and remaining terms to the right-hand side of the equation. So, we get:

$ax=c-b$ . Finally, the value of the variable $x$ is given by $x=\dfrac{c-b}{a}$.

For example: Consider the equation $x+9=13$ and compare with $ax+b=c$, we get:

$a=1, b=9$ and $c=13$.

Now, to find the value of the variable $x$, we will take all the terms containing the variable to the left-hand side of the equation and remaining terms to the right-hand side of the equation. So, we get

$x=13-9=4$. Hence, $x=4$ is the solution.

Now, coming to the given question, we are given $p+3=9$. To find the value of the variable $p$, we will take all the terms containing the variable to the left-hand side of the equation and remaining terms to the right-hand side of the equation. So, we get

$p=9-3=6$ . Hence, $p=6$ is the solution.

Hence, option B. is the correct answer.

Note: While shifting the constants from left-hand side of the equation to the right-hand side of the equation, do not forget to change the sign of the constant, i.e. if the sign is positive, change it to negative and vice-versa. Students generally forget to change the sign and end up getting a wrong answer.

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