Question

Pick out the solution from the values given in the bracket next to each equation. Show that the other values do not satisfy the equation.

(a) 5m = 60 (10, 5, 12, 15)

(b) n + 12 = 20 (12, 8, 20, 0)

(c) p − 5 = 5 (0, 10, 5 − 5)

(d) (7, 2, 10, 14)

(e) r − 4 = 0 (4, − 4, 8, 0)

(f) x + 4 = 2 (− 2, 0, 2, 4)

Answer 1

(a) 5m = 60

m = 12 is a solution to the given equation because for m = 12,

5m = 5 × 12 = 60 and hence, the equation is satisfied.

m = 10 is not a solution to the given equation because for m = 10,

5m = 5 × 10 = 50, and not 60

m = 5 is not a solution to the given equation because for m = 5,

5m = 5 × 5 = 25, and not 60

m = 15 is not a solution to the given equation because for m = 15,

5m = 5 × 15 = 75, and not 60

(b) n + 12 = 20

n = 8 is a solution to the given equation because for n = 8,

n + 12 = 8 + 12 = 20 and hence, the equation is satisfied.

n = 12 is not a solution to the given equation because for n = 12,

n + 12 = 12 + 12 = 24, and not 20

n = 20 is not a solution to the given equation because for n = 20,

n + 12 = 20 + 12 = 32, and not 20

n = 0 is not a solution to the given equation because for n = 0,

n + 12 = 0 + 12 = 12, and not 20

(c) p − 5 = 5

p = 10 is a solution to the given equation because for p = 10,

p − 5 = 10 − 5 = 5 and hence, the equation is satisfied.

p = 0 is not a solution to the given equation because for p = 0,

p − 5 = 0 − 5 = −5, and not 5

p = 5 is not a solution to the given equation because for p = 5,

p − 5 = 5 − 5 = 0, and not 5

p = −5 is not a solution to the given equation because for p = −5,

p − 5 = − 5 − 5 = −10, and not 5

(d)

q = 14 is a solution to the given equation because for q = 14,

and hence, the equation is satisfied.

q = 7 is not a solution to the given equation because for q = 7,

, and not 7

q = 2 is not a solution to the given equation because for q = 2,

, and not 7

q = 10 is not a solution to the given equation because for q = 10,

, and not 7

(e) r − 4 = 0

r = 4 is a solution to the given equation because for r = 4,

r − 4 = 4 − 4 = 0 and hence, the equation is satisfied.

r = −4 is not a solution to the given equation because for r = −4,

r − 4 = − 4 − 4 = −8, and not 0

r = 8 is not a solution to the given equation because for r = 8,

r − 4 = 8 − 4 = 4, and not 0

r = 0 is not a solution to the given equation because for r = 0,

r − 4 = 0 − 4 = −4, and not 0

(f) x + 4 = 2

x = −2 is a solution to the given equation because for x = −2,

x + 4 = − 2 + 4 = 2 and hence, the equation is satisfied.

x = 0 is not a solution to the given equation because for x = 0,

x + 4 = 0 + 4 = 4, and not 2

x = 2 is not a solution to the given equation because for x = 2,

x + 4 = 2 + 4 = 6, and not 2

x = 4 is not a solution to the given equation because for x = 4,

x + 4 = 4 + 4 = 8, and not 2