question_answer

(a) After 12 years I shall be 3 times as old as I was 4 years ago. Find my present age.

(b) Verify that \[x\text{ }=\text{ }4\]is a root of the equation \[2x-3=5.\]

Answer:

(a) Let                my present age = x years

After 12 years my age = (x + 12) years

4 years ago my age \[=\text{ }\left( x\text{ }-\text{ }4 \right)\]years

According to question,

\[x+12\text{ }=3\left( x-4 \right)\]

or                    \[x+12=3x-12\]

or                    \[x-3x=-12-12\]

or                     \[~-\text{ }2x=-24\]

or                         \[x=\frac{-24}{-2}\]

or                            \[x=12\]

Therefore, my present age = 12 years.

(b) Since            \[~2x-3\text{ }=5\]

Putting, x = 4 then

LHS \[=2x-3\]

\[=2\times 4-3=8-3=5\]

and                   RHS =5

Hence,              LHS = RHS = 5                         [Hence, Verified]