I. Translate the following phrases into algebraic expressions:
- The sum of x, y, and z.
- The product of a and b, divided by the sum of c and d.
- Three times the square of x minus five.
- The square root of the quantity m plus n.
- A number n increased by seven, then multiplied by two.
II. Evaluate the following if a = 2, b = 3, and c = 5:
- 3a + 2b
- c² − (a + b)
- (10a) / c
- ab + bc + ac
- (c − a)²
III. Word Problems:
- If a man is x years old now, how old was he 5 years ago?
- A rectangle has a length of l and a width of w. Write an expression for its perimeter.
I. Expressions:
- x + y + z
- ab / (c + d)
- 3x² − 5
- √(m + n)
- 2(n + 7)
II. Evaluations:
- 3(2) + 2(3) = 6 + 6 = 12
- 5² − (2 + 3) = 25 − 5 = 20
- 20 / 5 = 4
- 6 + 15 + 10 = 31
- (5 − 2)² = 3² = 9
III. Word Problems:
- x − 5
- 2l + 2w (or 2(l + w))