Question

Solve $ 5x=3x+24 $ for the value of x.

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 x, eliminate the terms so as to have all the terms containing the variable 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 x which satisfies the equation.

Complete step by step solution:
The given equation is $ 5x=3x+24 $ .

Subtracting $ 3x $ from both sides of the equation, we get:
⇒ $ 2x=24 $

Dividing both sides by 2, we get:
⇒ $ x=12 $ , which is the required solution.

Check:
$ 5(12)=3(12)+24 $
⇒ $ 60=36+24 $
⇒ $ 60=60 $

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