[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
- By substitution, justify that x = − 6 is a solution to x − 2 = − x − 14.
[tex] \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}[/tex]
First, let's substitute the value of x as -6 in the equation.
[tex] \tt \: x - 2 = - x - 14 \\ \dashrightarrow \: \tt \: ( - 6) - 2 = - ( - 6) - 14[/tex]
Now, let's solve it.
[tex] \tt \: ( - 6 ) - 2 = - ( - 6 ) - 14[/tex]
Subtract 2 from -6 to get -8.
[tex] \tt \: -8=-\left(-6\right)-14 [/tex]
The opposite of -6 is 6.
[tex] \tt \: -8=6-14 [/tex]
Subtract 14 from 6 to get -8.
[tex] \tt \: -8=-8 [/tex]
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.
