Question

Solve the following equation:
\[3\left( t-3 \right)=5\left( 2t-1 \right)\]

Answer 1

Hint: Consider the linear equation then make the variables as subjects or take variables to one side and constant term to the other and hence find the value of variable ‘t’.

Complete step-by-step answer:
We are given a linear equation \[3\left( t-3 \right)=5\left( 2t-1 \right)\] and we have to find the value of t.
First we will understand what are linear equations and learn some facts about them.
Let a linear equation can be written in form of,
\[ax+b=0\]
Where a and b are real numbers and x is a variable. This form is sometimes called the standard form of linear equations. Please note that most linear equations will not start of this form. Also the variable may or may not be an x or please don’t get too locked into always seeing x there.
Now for solving linear equations we will make heavy use of facts which are,
(i) If a = b then a + c = b + c for any value of c. All this saying is that we can add a number c to both the sides of the equation and not change the equation.
(ii) If a = b then a – c = b – c for any value of c. All this saying is that we can subtract a number c to both the sides of the equation and not change the equation.
(iii) If a = b then ac = bc for any non-zero value of c, so that the value of the equation remains unaltered.
(iv) If a = b, then \[\dfrac{a}{c}=\dfrac{b}{c}\] for any non – zero value of c, so that the value of the equation remains unaltered.
These points are very important and help very much while solving any linear type of equations they should be kept in mind.
So, the given linear equation is:
\[3\left( t-3 \right)=5\left( 2t-1 \right)\]
Now we will expand by multiply in the respective sides of equation so we get,
3t – 9 = 10t – 5
Now adding 9 to both the sides of equation so we get,
3t – 9 + 9 = 10t + 4 – 10t
Or, -7t = 4
So, the value of t = \[\dfrac{-4}{7}\].

Note: Students confuse themselves if they see any other variable other than x as they don’t have a habit to see it. Also they should follow all the rules of linear equations.