Question

How do you solve the equation $\sqrt{2x-3}=2$ ?

Answer 1

Hint: Now we are given with a linear equation in x. we want to find the value of x which satisfies the equation. Now we will first eliminate the square root in the equation by squaring the equation on both sides. Now we will separate the constant terms and the variable terms in the equation. Now on simplifying the obtained equation we will be able to write the equation in the form of $ax=b$ . Now to find the value of x we will divide the whole equation by coefficient of x.

Complete step by step solution:
Now consider the given equation $\sqrt{2x-3}=2$ .
We want to find the solution to this equation. Now the equation is a linear equation in x. first we will have to write it in the form $ax=b$ .
Now we have a square root in the equation. First we will try to eliminate the square root.
To eliminate the square root we will square the equation on both sides.
$\Rightarrow {{\left( \sqrt{2x-3} \right)}^{2}}={{2}^{2}}$
Now we know that ${{\left( \sqrt{a} \right)}^{2}}=a$ hence using this we get,
$\Rightarrow 2x-3=4$
Now adding 3 on both sides we get,
$\begin{align}
  & \Rightarrow 2x-3+3=4+3 \\
 & \Rightarrow 2x=7 \\
\end{align}$
Now to find the value of x we will divide the whole equation by coefficient of x hence we get,
$\Rightarrow x=\dfrac{7}{2}$
Hence we get the solution of the equation as $x=\dfrac{7}{2}$ .

Note: Now note that when we have square root in the equation then we first separate square root and all other terms in the equation and square the equation. Similarly if we have a square in equation we can separate the square terms and other terms and take square root on both sides.