For x = 5 and y = 2, verify the following:

(i) (x + y)² = x² + 2xy + y²

(ii) (x - y)² = x² - 2xy + y²

(iii) x² - y² = (x + y)(x - y)

(iv) (x + y)² = (x - y)² + 4xy

(v) (x + y)³ = x³ + y³ + 3x²y + 3xy²

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 the following linear equations:

(i) 5(x + 1) = 25

(ii) 2(3x − 1) = 10

(iii) $\dfrac{3x - 1}{4} = 11$

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