Equations--inequalities-and-identities.doc

Math Exercise on Equalities and Inequalities for Grade 7

1. Equations, identities and inequalities
Label the following as either
equations, identities or inequalities:

1) 3x + 1 = 4

2) x + 2 > 5

3) x² = 2x + 3

4) 5x(x – 2) ≡ 5x² - 10x

5) a² - b² ≡ (a + b)(a – b)

6) 7x + 4 < 4 – 2x

7) 4x² + 3x + 3 = 7

8) x(x+4) – 2x² ≡ 4x - x²

9) 8x² + 2x – 15 ≡ (2x + 3)(4x - 5)

10) x² - x + 5 > 5x - 6
Red: I can identify and recognise
equations, identities and
inequalities
Amber: I can prove algebraic
identities
Green: I can find missing values in
algebraic identities
Prove these identities:

1) 3(x + 2) + 4(x – 1) ≡ 7x + 2

2) 5(x – 2) + 3(x – 3) ≡ 8x – 19

3) 8(x + 4) + 5(x – 2) ≡ 13x + 22

4) x(x + 4) – 3(4 + x) ≡ x² + x - 12

5) x(x + 3) + 2(x + 3) ≡ x² + 5x +
6

6) 5(x + 2) - 3(x + 4) ≡ 2(x – 1)

7) 4(x + 2) + 2(x + 1) ≡ 2(3x + 5)

8) x(x – 4) + x(x + 2) ≡ 2x(x - 1)

Find the missing values:

1) 2(x + 2) + 5(x + 1) ≡ □x + □

2) 3(x – 2) + 4(x + 3) ≡ □x + □

3) 5(x + □) + 3(x - □) ≡ 8x – 19

4) x(x + □) + 2(x + □) ≡ x² + 3x + 4

5) x(x – 4) + 2x(x – 3) ≡ □x² - □x

6) x(2x + □) ≡ □x² + 6x

7) □x(3x + 2) ≡ 12x² + □x

8) □x(□x – 5) ≡ 16x² - 20x

9) 6(2x - □) + 3(□x – 4) ≡ 15x – 24

10) 7(7x - □) + 2x(□x + 9) ≡ 6x² +
□x - 56

2. Substituting into formulae
1) Equation

2) Inequality

3) Equation

4) Identity

5) Identity

6) Inequality

7) Equation

8) Identity

9) Identity

10) Inequality

Red answers: Amber answers: Green answers:
Proofs: Expand brackets to show that
the Right Hand Side equals the Left
Hand Side

1) 2(x + 2) + 5(x + 1) ≡ 10x + 9

2) 3(x – 2) + 4(x + 3) ≡ 7x + 6

3) Possible answer: 5(x + 1) + 3(x –
8)

4) x(x + 1) + 2(x + 2) ≡ x² + 3x +
4

5) x(x – 4) + 2x(x – 3) ≡ 3x² - 10x

6) x(2x + 6) ≡ 2x² + 6x

7) 4x(3x + 2) ≡ 12x² + 8x

8) 2x(8x – 5) ≡ 16x² - 20x

9) 6(2x - 4) + 3(4x – 4) ≡ 15x – 24

10) 7(7x - 8) + 2x(3x + 9) ≡ 6x² +
67x - 56