Substitution

Substitution is simply when we relace every instance of a variable in an expression with a value we know.

For example, we may be asked to work out the value of an expression when x= a certain value.

Steps

1. Replace every instance of the variable in the expression with the given value - put this value inside brackets to avoid mistakes with negative numbers.
2. Evaluate the expression by just calculating the expression as normal. Make sure to follow the order of operations.

Examples

Find the value of 2x + 3 when x = 4

• Replace x with (4):
  • 2(4) + 3
• Evaluate the expression:
  • 2 \times 4 + 3
  • 8 + 3
  • 11
• Answer: 11

Find the value of x^2 - 5x + 6 when x = 3

• Replace x with (3):
  • (3)^2 - 5(3) + 6
• Evaluate the expression:
  • 9 - 15 + 6
  • -6 + 6
  • 0
• Answer: 0

Find the value of 3y^2 + 2y - 4 when y = -2

• Replace y with (-2):
  • 3(-2)^2 + 2(-2) - 4
• Evaluate the expression:
  • 3 \times 4 + (-4) - 4
  • 12 - 4 - 4
  • 8 - 4
  • 4
• Answer: 4

Find the value of \frac{2a + 5}{a - 1} when a = 6

• Replace a with (6):
  • \frac{2(6) + 5}{(6) - 1}
• Evaluate the expression:
  • \frac{12 + 5}{6 - 1}
  • \frac{17}{5}
• Answer: \frac{17}{5}

Find the value of 4b^2 - 3b + 2 when b = \frac{1}{2}

• Replace b with \left(\frac{1}{2}\right):
  • 4\left(\frac{1}{2}\right)^2 - 3\left(\frac{1}{2}\right) + 2
• Evaluate the expression:
  • 4 \times \frac{1}{4} - \frac{3}{2} + 2
  • 1 - \frac{3}{2} + 2
  • 3 - \frac{3}{2}
  • \frac{6}{2} - \frac{3}{2}
  • \frac{3}{2}
• Answer: \frac{3}{2}

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