Question

Solve each of the following equations. Also verify in each case.
$3x-2\left( 2x-5 \right)=2\left( x+3 \right)-8$

Answer 1

Hint: Solve the expression and find the value of x. To verify it, take LHS and RHS of the given expression, separately and put the values of x. Now, prove that LHS is equal to RHS.

Complete step-by-step answer:
We have been given an equation, consisting of only one variable ‘x’. Now let us solve the given equation and get the value of x.
The given equation is
$3x-2\left( 2x-5 \right)=2\left( x+3 \right)-8$ …………………………………………(1)
Let us rearrange the above equation and simplify it,
$3x-\left( 2\times 2x \right)+\left( 2\times 5 \right)=2x+\left( 2\times 3 \right)-8$
$3x-4x+10=2x+6-8$
$\Rightarrow -x+10=2x-2$
Now let us rearrange the values
$2x+x=10+2$
$\Rightarrow 3x=12$
$\therefore x=\dfrac{12}{3}=4$
Thus, we got the values of x as 4. Now we are asked to verify the expression. To undergo the verification, put $x=4$ in equation (1).
First let us take the LHS of (1) and put $x=4$
$3x-2\left( 2x-5 \right)=\left( 3\times 4 \right)-2\left( 2\times 4-5 \right)$
$=12-2\left( 8-5 \right)$
$=12-2\times 3=12-6=6$
Thus, we got LHS $=6$ .
Now, let us put $x=4$ in the RHS of (1)
$2\left( x+3 \right)-8=2\left( 4+3 \right)-8=2\times 7-8$
$=14-8=6$
Thus, we got RHS $=6$ .
Hence, from this we can say that $LHS=RHS=6$
Thus, we have verified the equation, and in the result we got LHS equal to RHS.

Note: You can also prove that LHS is equal to RHS in a few steps, rather than proving it both separately. You will get the final result as $LHS=RHS=6$ . Be careful while solving and carry out the arithmetic operation without mistake.