Mathematics 10 — Exercise 4.1 · Q1 (i)

Full question

For the following functions, find f+g.

Step-by-step solution

1. Substitute the function expressions, keeping the brackets.

   $$2\times x+5+3\times x-2$$

2. Remove the brackets. A preceding minus sign reverses every sign inside that bracket.

   $$2\times x+5+3\times x-2$$

3. Write EVERY distributed product before collecting terms.

   $$5+2\times x-2+3\times x$$

4. Calculate this individual product, including its sign and powers.

   $$5=5$$

5. Calculate this individual product, including its sign and powers.

   $$2\times x=2\times x$$

6. Calculate this individual product, including its sign and powers.

   $$-2=-2$$

7. Calculate this individual product, including its sign and powers.

   $$3\times x=3\times x$$

8. These terms have the same variable part. Add ONLY their coefficients.

   $$5-2=3$$

9. These terms have the same variable part. Add ONLY their coefficients.

   $$2+3=5$$

10. Put the simplified groups together.

    $$5\times x+3$$

11. Collect terms with the same power and simplify their coefficients.

    $$5\times x+3$$

Answer

The final answer is shown below.