Question

What is the value of the expression (3a-b)/(6(b+a)) when a = 5 and b = -3?

Show your work.

Answer 1

• 1.5 or 1½

Task :

• To evaluate the expression (3a-b)/6(b+a) when a = 5 and b = -3

Solution :

All we need to do is plug in the respective value of a and b in the expression given and solve for it .

• 
  `\rightarrow ((3a - b))/(6(a + b)) \\`

• 
  `\rightarrow (3a \: - b)/(6a \: + 6b) \\`

• 
  `\rightarrow (3 (5) \: - ( - 3))/(6(5) \: + 6( - 3)) \\`

• 
  `\rightarrow (15 \: + 3)/(30 \: - 18) \\`

• 
  `\rightarrow (18)/(12) = ( 3)/(2) \\`

• 
  `\rightarrow 1 (1)/(2) \: or \: 1.5 \\`

Thus, the value of the expression is 1½ or 1.5 .

Answer 2

`\sf ( 3)/(2) \textsf{ or } 1 (1)/(2) \textsf{ or } 1.5`

Explanation:

`\sf (3a-b)/(6(b+a))`

In order to find the value of the expression when a = 5 and b = -3, we can simply by substituting the values of a and b into the expression and evaluate.

`\begin{aligned} \sf (3a-b)/(6(b+a)) &= (3(5)-(-3))/(6((-3)+5)) \\\\ &= (15+3)/(6(2)) \\\\ &=( 18)/(12) \\\\ &=\frac{\cancel{6} \cdot 3 }{\cancel{3}\cdot 2 } \\\\ &= ( 3)/(2) \textsf{ or } 1 (1)/(2) \textsf{ or } 1.5 \end{aligned}`

Therefore, the value of the expression is:

`\sf ( 3)/(2) \textsf{ or } 1 (1)/(2) \textsf{ or } 1.5`