Fill in the blanks :

(i) An equation involving one variable with highest power ……………, is called a linear equation in that variable.

(ii) The solution of an equation is also called …………… of the given equation.

(iii) The process in which we drop a term from one side of an equation and put it on the other side with sign changed is called …………… .

(iv) A linear equation can have at the most …………… solution(s).

(v) If thrice a number increased by 8 gives 23, then the number is …………… .

(vi) If x - 7 = 4, then 3x - 15 is equal to …………… .

(i) An equation involving one variable with highest power 1, is called a linear equation in that variable.

(ii) The solution of an equation is also called root of the given equation.

(iii) The process in which we drop a term from one side of an equation and put it on the other side with sign changed is called transposition.

(iv) A linear equation can have at the most 1 solution(s).

(v) If thrice a number increased by 8 gives 23, then the number is 5.

(vi) If x - 7 = 4, then 3x - 15 is equal to 18.

Explanation

(i) A linear equation is defined by the fact that the variable has an exponent of 1. If the power were 2, it would be a quadratic equation.

(ii) In algebra, the specific value of the variable that makes the equation true (LHS = RHS) is formally called the "root" or the solution.

(iii) Transposition is the mathematical term for moving terms across the equal sign (=) while reversing their operation (plus becomes minus, multiply becomes divide).

(iv) A linear equation in one variable can have at the most one solution.

(v)

Let the number be x.

According to the condition:

3x + 8 = 23

⇒ 3x = 23 - 8 $\quad$ [Transposing +8 to RHS]

⇒ 3x = 15

⇒ x = $\dfrac{15}{3}$

⇒ x = 5

∴ The required number is 5.

(vi)

Given equation:

x - 7 = 4

First, find the value of x:

x - 7 = 4

⇒ x = 4 + 7 $\quad$ [Transposing -7 to RHS]

⇒ x = 11

Now, substitute x = 11 into the expression 3x - 15:

3x - 15 = 3(11) - 15

= 33 - 15

= 18

∴ 3x - 15 = 18