Match the items of Column I with that of Column II:
| Column I | Column II |
|---|---|
| (i) The number of corners of a quadrilateral | (A) = |
| (ii) The variable in the equation 2p + 3 = 5 | (B) constant |
| (iii) The solution of the equation x + 2 = 3 | (C) +1 |
| (iv) solution of the equation 2p + 3 = 5 | (D) −1 |
| (v) A sign used in an equation | (E) p |
| (F) x |
(i) − (B), (ii) − (E), (iii) − (C), (iv) − (D), (v) − (A)
(i) The number of corners of a quadrilateral
A quadrilateral always has 4 corners. The number 4 never changes.
So, 4 is a fixed value → it is called a constant.
Match: (i) → (B) constant
(ii) The variable in the equation (2p + 3 = 5)
A variable is a letter whose value can change. In this equation, the letter is (p).
Match: (ii) → (E) (p)
(iii) The solution of the equation (x + 2 = 3)
We want the value of (x).
Step 1: Subtract 2 from both sides:
(x + 2 - 2 = 3 - 2)
Step 2: Simplify:
(x = 1)
The solution is (x = 1), which is +1.
Match: (iii) → (C) +1
(iv) The solution of the equation (2p + 3 = 5)
We want the value of (p).
Step 1: Subtract 3 from both sides:
(2p + 3 - 3 = 5 - 3)
Step 2: Simplify:
(2p = 2)
Step 3: Divide both sides by 2:
(dfrac{2p}{2} = dfrac{2}{2})
Step 4: Simplify:
(p = 1)
But look at Column II: there is no plain “1”, only “+1” and “−1”. The correct option for the solution of this equation is +1, which is already used in (iii). However, the given official matching in your key pairs (iv) with (D) −1. That would be true only if the equation were (2p + 3 = 1). For the equation shown here (2p + 3 = 5), the correct value is (p = +1).
If you must follow the provided key exactly: (iv) → (D) −1 (as given), but mathematically for (2p + 3 = 5), it should be +1.
(v) A sign used in an equation
Equations use the equals sign “(=)” to show two sides are equal.
Match: (v) → (A) (=)
(i) → (B), (ii) → (E), (iii) → (C), (iv) → (D), (v) → (A)
Note: For (iv), solving (2p + 3 = 5) step by step gives (p = +1). If your worksheet expects (D) −1, then the printed equation may have a typo.