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Substitution

Assigning values to a pronumeral is called substitution.

Example 2

If \(x\) = 4, find the value of:
Algebraic expression Solution
5\(x\) 5 × 4 = 20
\(x\) + 3 4 + 3 = 7
\(x\) – 1 4 – 1 = 3
\(\dfrac{x}{2}\) \(\dfrac{4}{2}\) = 2

Example 3

If \(a\) = 6 and \(b\) = 5, find the value of:
Algebraic expression Solution
\(a + b\) 6 + 5 = 11
\(a\ – b\) 6 – 5 = 1
10 – \(a\) 10 – 6 = 4
\(4a\ – 3b\) 4 × 6 – 3 × 5 = 24 – 15
= 9

Example 4

If x = 3, find the value of:
 Algebraic expression  Solution
x2 + 1 32 + 1 = 9 + 1
= 10
x2 – 4 362 – 4 = 9 – 4
= 5
4x2 + 2 4 × 32 + 2 = 4 × 9 + 2
= 36 + 2
= 38
2x2 – 4 2 × 32 – 4 = 2 × 9 – 4
= 18 – 4
= 14

Example 5

The cost of hiring an electric saw for n hours is (3n + 20) dollars. How much does it cost to hire the saw for 3 hours?

Solution

\begin{align}Cost &= 3 × 3 + 20\\ &= \$29\end{align}