Equation or identity?

The Maths Habit

  1. Expand 7(x + 4)

    7x + 28

  2. Expand 3(2y − 5)

    6y − 15

  3. Expand 2(5p + 1)

    10p + 2

Always, sometimes or never true?

  1. Add 0 to a number and it stays the same.

    Always

  2. A number times 3 is 12.

    Sometimes

  3. A number add 1 is the same as the number.

    Never

Equation
True for some values of the letter.
Identity
True for every value of the letter.

=equal for some values ≡equal for every value

x3x + 1x + 5
1
2
3

Equation or identity?

x3(x + 2)3x + 6
199
21212
31515

Identity

Equation or identity?

x2x + 4x + 6
1
2
3

Equation

Equation or identity?

x3(x + 2)3x + 6
1
2
3

Identity

Equation or identity?

x5(x − 1)5x − 5
1
2
3

Identity

Show that the two sides are identical

4(x + 1) + 2x ≡ 6x + 4

Equation or identity? worksheet, page 1

Equation or identity? worksheet, page 2

Answer sheet

  1. 4(x + 3) + 2(x − 1) ≡ ax + b. Find a and b.

    a = 6, b = 10

  2. Show that 3(x + 4) − 2(x + 1) ≡ x + 10

    3x + 12 − 2x − 2

  1. A  6x − 1 = 2x + 7    B  4(x + 2) − x = 3x + 8
    Which is an equation and which is an identity?

    A equation, B identity

  2. Show that 3(x + 4) − 5 ≡ 3x + 7

    3x + 12 − 5 = 3x + 7

  3. Is 2(x + 3) + 4x ≡ 6x + 3 true? Show how you know.

    No: it is 6x + 6
Exit tickets to print