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.

Answer 2

Hey there!

x - 2 = -x - 14

Substitute -6 for x (given).

x - 2 = -x - 14

= (-6) - 2 = -(-6) - 14

= -8 = +6 - 14

= -8 = -8

The Left Hand Side (LHS) is equal to the Right Hand Side (RHS).

•°• LHS = RHS, hence proved.

Hope it helps ya!