Quick 10

Study session

1. Question: Expand $(x-3{)}^2$.

   Answer: $x^2-6x+9$.

2. Question: Write $x\ge 3$ in interval notation.

   Answer: $[3,\mathrm{\infty })$.

3. Question: What keeps an equation balanced?

   Answer: Apply the same valid operation to both sides.

4. $x+x^2=2x^2$ for all real x.

   False. x and $x^2$ are not like terms; at $x=2$ the values are 6 and 8.

5. Multiplying two binomials only requires the first and last products.

   False. The cross-products are also needed before combining like terms.

6. Subtracting 4 from both sides of an equation preserves equality.

   True. The same subtraction keeps both sides balanced.

7. Dividing an inequality by −2 preserves its direction.

   False. Division by a negative number reverses the direction.

8. Checking one input is enough to prove an algebraic identity.

   False. Different expressions can agree at one input and disagree at others.

9. Question: Simplify $4x+6x$.

   Answer: $10x$.

10. Question: What does simplifying an expression mean?

    Answer: Rewrite it in an equivalent, more usable form.