Now can you simplify these?

(i) (x + 4) + (x − 2)

(ii) (2x + 3) + (x − 1)

(iii) (x + 1) + (x − 1)

(iv) (5x + 6y) + (2x − 3y)

(v) (x + y) + (x − y)

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Solution

(i) (x + 4) + (x − 2)

= (x + 4 + x) − 2 [for any three numbers x, y, z, with y > z, x + (y − z) = (x + y) − z]

= (2x + 4) − 2

= 2x + (4 − 2)

= 2x + 2

= 2(x + 1)

(ii) (2x + 3) + (x − 1)

= (2x + 3 + x) − 1 [for any three numbers x, y, z, with y > z, x + (y − z) = (x + y) − z]

= (3x + 3) − 1

= 3x + (3 − 1)

= 3x + 2

(iii) (x + 1) + (x − 1)

= (x + 1 + x) − 1 [for any three numbers x, y, z, with y > z, x + (y − z) = (x + y) − z]

= (2x + 1) − 1

= 2x + (1 − 1)

= 2x + 0

= 2x

(iv) (5x + 6y) + (2x − 3y)

= (5x + 6y + 2x) − 3y [for any three numbers x, y, z, with y > z, x + (y − z) = (x + y) − z]

= (7x + 6y) − 3y

= 7x + (6y − 3y)

= 7x + 3y

(v) (x + y) + (x − y)

= (x + y + x) − y [for any numbers x, y, z, with y > z, x + (y − z) = (x + y) − z]

= (2x + y) − y

= 2x + (y − y)

= 2x + 0

= 2x

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Similar questions

Now can’t you simplify these?

(i) (2x − 1) + (x − 2)

(ii) (5x − 6y) + (2x − 3y)

(iii) (2x − 3y) + (3x − 2y)

(iv) (x − y) + (x − y)

Now can’t you simplify these?

(i) 2x + (3x + 1)

(ii) x + (2x + 3)

(iii) (x + 2) + (2x + 1)

(iv) (x + 1) + (x + y)

(v) (3x + 2y) + (x + y)

(vi) (3x + 2y) + (2x + 3y)

Now can you write the meaning of the expressions below in ordinary language?

(i)

(ii)

(iii)

(iv)

(v) x + y + 2

(vi)

(vii) ab + 1

(viii) (a + 1) (b + 1)

(x^{3} - 2 x^{2} + 3 x - 4) (x - 1) - (2 x - 3) (x^{2} - x + 1)

x^{2} (x - y) y^{2} (x + 2 y)

[{5 x - (x + 3 y)} - {x + (2 x - y)}]

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