Simple Equation

Exercise 4.3

Question 1: Solve the following equations:

(a) `2y+5/2=(35)/(2)`

Answer: `2y+5/2=(35)/(2)`

Or, `2y=(35)/(2)-5/2`

Or, `2y=(35-7)/(2)=(28)/(2)=14`

Or, `y=(14)/(2)=7`

(b) `5t+28=10`

Answer: `5t+28=10`

Or, `5t=10-28=-18`

Or, `t=-(18)/(5)=-33/5`


(c) `a/5+3=2`

Answer: `a/5+3=2`

Or, `a/5=2-3=-1`

Or, `a=-1xx5=-5`

(d) `q/4+7=5`

Answer: `q/4+7=5`

Or, `q/4=5-7=-2`

Or, `q=-2xx4=-8`

(e) `5/2x=10`

Answer: `5/2x=10`

Or, `x=10xx2/5=4`

(f) `5/2x=(25)/(4)`

Answer: `5/2x=(25)/(4)`

Or, `x=(25)/(4)xx2/5=5/2=21/2`


(g) `7m+(19)/(2)=13`

Answer: `7m+(19)/(2)=13`

Or, `7m=13-(19)/(2)`

Or, `7m=(26-19)/(2)=7/2`

Or, `m=7/2÷7=1/2`

(h) `6z+10=-2`

Answer: `6z+10=-2`

Or, `6z=-2-10=-12`

Or, `z=-(12)/(6)=-2`

(i) `(3l)/(2)=2/3`

Answer: `(3l)/(2)=2/3`

Or, `3l=2/3xx2=4/3`

Or, `l=4/3÷3=4/9`

(j) `(2b)/(3)xx5=3`

Answer: `(2b)/(3)xx5=3`

Or, `(2b)/(3)=3/5`

Or, `b=3/5xx3/2=(9)/(10)`

Question 2: Solve the following equations:

  1. `2(x + 4) = 12`

    Answer: `2(x + 4) = 12`
    Or, `x + 4 = 12 ÷ 2 = 6`
    Or, `x = 6 – 4 = 2`
  2. `3(n – 5) = 21`

    Answer: `3(n – 5) = 21`
    Or, `n – 6 = 21 ÷ 3 = 7`
    Or, `n = 7 + 6 = 13`
  3. `3(n – 5) = - 21`

    Answer: `3(n – 5) = - 21`
    Or, `n – 5 = - 21 ÷ 3 = - 7`
    Or, `n = - 7 + 5 = - 2`
  4. `– 4(2 + x) = 8`

    Answer: `– 4(2 + x) = 8`
    Or, `2 + x = 8 ÷ ( - 4) = - 2`
    Or, `x = - 2 – 2 = - 4`
  5. `4(2 – x) = 8`

    Answer: `4(2 – x) = 8`
    Or, `2 – x = 8 ÷ 4 = 2`
    Or, `x = 2 – 2 = 0`

Question 3: Solve the following equations:

  1. `4 = 5(p – 2)`

    Answer: `4 = 5(p – 2)`
    Or, `p – 2 = 4 ÷ 5 = 0.8`
    Or, `p = 0.8 + 2 = 2.8`
  2. `– 4 = 5(p – 2)`

    Answer: `– 4 = 5(p – 2)`
    Or, `p – 2 = - 4 ÷ 5 = - 0.8`
    Or, `p = - 0.8 + 2 = 1.2`
  3. `16 = 4 + 2(t + 2)`

    Answer: `16 = 4 + 2(t + 2)`
    Or, `2(t + 2) = 16 – 2 = 14`
    Or, `t + 2 = 14 ÷ 2 = 7`
    Or, `t = 7 – 2 = 5`
  4. `4 + 5(p – 1) = 34`

    Answer: 4 + 5(p – 1) = 34
    Or, `5(p – 1) = 34 – 4 = 30`
    Or, `p – 1 = 30 ÷ 5 = 6`
    Or, `p = 6 + 1 = 7`
  5. `0 = 16 + 4(m – 6)`

    Answer: 0 = 16 + 4(m – 6)
    Or, `4 (m – 6) 0 – 16 = - 16`
    Or, `m – 6 = - 16 ÷ 4 = - 4`
    Or, `m = - 4 + 6 = 2`

Question 4: Construct three equations starting with `x = 2`

Answer: `x + 2 = 4`
`2x + 3 = 7`
`3x – 2 = 4`

Quesiton 5: Construct three equations starting with `x = - 2`

Answer: `2x – 3 = -7`
`2x + 4 = 0`
`5x + 12 = 0`



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