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) 5*m*
= 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)

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Solution

(a) 5*m*
= 60

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

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

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

5*m* = 5 × 10 = 50, and not 60

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

5*m* = 5 × 5 = 25, and not 60

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

5*m* = 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

0

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