State which of the following are equations with a variable. In case of an equation with a variable, identify the variable.

(i) 17 + x = 5

(ii) 2b − 3 = 7

(iii) (y - 7) > 5

(iv) $\dfrac{9}{3} = 3$

(v) 7 × 3 − 19 = 2

(vi) 5 × 4 − 8 = 3t

(vii) 2p < 15

(viii) 7 = 11 × 5 − 12 × 4

(ix) $\dfrac{3}{2}q = 5$

Solve each of the following linear equations:

(i) x + 6 = 8

(ii) x − 2 = −5

(iii) 4x = 6

(iv) $\dfrac{x}{2} = 5$

(v) 2y − 3 = 2

(vi) 5y + 2 = 4

Solve the following linear equations:

(i) 5x − 6 = 12 − x

(ii) $\dfrac{n}{3} + 1 = 4 - n$

(iii) 5p + 7 = 19 − 2p

(iv) $2x + \dfrac{2}{3} = \dfrac{5}{2} - x$

(v) $\dfrac{x}{2} - 5 = \dfrac{x}{3} - 4$

(vi) $18 - \dfrac{3y}{4} = 11 + y$

Fill in the blanks:

(i) In algebra, we use ….. to represent variables (generalized numbers).

(ii) A symbol or letter which can be given various numerical values is called a …..

(iii) If Jaggu's present age is x years, then his age 7 years from now is …..

(iv) If one pen costs ₹x, then the cost of 9 pens is …..

(v) An equation is a statement that the two expressions are ……

(vi) The numerical coefficient of the monomial −5x²y³ is …..

(vii) 7 less than thrice a number y is …..

(viii) If 3x + 4 = 19, then the value of x is …..

(ix) The number of pencils bought for ₹x at the rate of ₹2 per pencil is ……… .

(x) 3p²q and −5pq² are ….. terms.

(xi) The value of the expression 3 − 5x for x = 4 is …..