Question

Find the numerical value of each expression where a= -3 and b = 1/2 d) -a -2/3 b +a e) 1/6 a + b² + b f) -2a + 3b- (b-a) ​

Answer 1

To find the numerical value of each expression, we substitute the given values of a and b into the expressions and perform the operations.

d) -a - 2/3 b + a

Substituting a = -3 and b = 1/2:

-(-3) - 2/3(1/2) + (-3)

= 3 - 1/3 - 3

= 9/3 - 1/3 - 9/3

= (9 - 1 - 9)/3

= -1/3

So, -a - 2/3 b + a = -1/3.

e) 1/6 a + b² + b

Substituting a = -3 and b = 1/2:

1/6(-3) + (1/2)² + (1/2)

= -1/2 + 1/4 + 1/2

= -2/4 + 1/4 + 2/4

= (-2 + 1 + 2)/4

= 1/4

So, 1/6 a + b² + b = 1/4.

f) -2a + 3b - (b - a)

Substituting a = -3 and b = 1/2:

-2(-3) + 3(1/2) - (1/2 - (-3))

= 6 + 3/2 - (1/2 + 3)

= 6 + 3/2 - (1/2 + 6)

= 6 + 3/2 - (7/2)

= 6 + 3/2 - 7/2

= (12 + 3 - 7)/2

= 8/2

= 4

So, -2a + 3b - (b - a) = 4.