Question

By substitution, justify that x= − 6 is a solution to x − 2 = − x − 14

Answer 1

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

• By substitution, justify that x = − 6 is a solution to x − 2 = − x − 14.

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

First, let's substitute the value of x as -6 in the equation.

$\tt \: x - 2 = - x - 14 \\ \dashrightarrow \: \tt \: ( - 6) - 2 = - ( - 6) - 14$

Now, let's solve it.

$\tt \: ( - 6 ) - 2 = - ( - 6 ) - 14$

Subtract 2 from -6 to get -8.

$\tt \: -8=-\left(-6\right)-14$

The opposite of -6 is 6.

$\tt \: -8=6-14$

Subtract 14 from 6 to get -8.

$\tt \: -8=-8$

Compare -8 and -8. We can see that both the LHS & RHS are equal to each other. So, hence we proved that x = − 6 is a solution of x − 2 = − x − 14.