Question

How do you solve $ 12-x=-4 $ ?

Answer 1

Hint:
Remember that we can add / subtract or multiply / divide both sides of the equation by the same number, without affecting the equality. To find the value of the variable (x), eliminate the terms so as to have all the terms containing the variable (x) on one side and the constants (numbers) on the side of the equality. Since this is a linear equation, there will be a single value of the variable (x) which satisfies the equation.

Complete Step by step Solution:
Following the rules of equalities, we can subtract 12 from both sides of the equation $ 12-x=-4 $ , to get:
⇒ $ (12-x)-12=-4-12 $
⇒ $ -x=-16 $
On multiplying (or dividing) both sides by −1, we get:
⇒ $ (-x)(-1)=(-16)(-1) $
⇒ $ x=16 $ , which is the required solution.
We can also check our answer as:
LHS = 12 − 16 = −4 = RHS

Note:
Rules of equality:
1) Equal quantities remain equal if the same number is added / subtracted to both of them.
2) Equal quantities remain equal if both are multiplied / divided by the same real number.
3) If $ ab=0 $ , then $ (a=0\ AND\ b\ne 0) $ OR $ (a\ne 0\ AND\ b=0) $ OR $ (a=0\ AND\ b=0) $ .
Rules of inequality:
1) The order of the inequality does not change if the same quantity is added / subtracted to both the quantities.
2) The order of the inequality does not change if both the quantities are multiplied / divided by the same "positive" real number.
3) The order of the inequality reverses if both the quantities are multiplied / divided by the same "negative" real number.
4) If $ ab>0 $ , then $ (a>0\ AND\ b>0) $ OR $ (a<0\ AND\ b<0) $ .
5) If $ ab<0 $ , then $ (a>0\ AND\ b<0) $ OR $ (a<0\ AND\ b>0) $ .