Algebra Homework 3.1 – Key Concepts & Practice

When solving a linear inequality, what must you do to the inequality sign if you multiply or divide by a negative number?

Reverse (flip) the direction of the inequality sign.

Solve and state in interval notation: −3u < 9 or 4u − 1 ≥ 3.

u > −3 is already satisfied by u ≥ 1; the union is (−3, ∞).

How do you find the x-intercept of the line 5x − 2y = 10?

Set y = 0 and solve for x: 5x = 10 → x = 2.

What are the intercepts of 5x − 2y = 10?

x-intercept (2, 0) and y-intercept (0, −5).

What is the slope of y = 5 − 8x, and what slopes are parallel and perpendicular to it?

Slope m = −8. Parallel lines have slope −8. Perpendicular lines have slope 1/8 (the negative reciprocal).

What is the relationship between the slopes of two perpendicular lines in the plane?

Their slopes are negative reciprocals: m₁·m₂ = −1.

Set up and solve: 5 lb jelly beans + 3 lb almonds cost $20; 7 lb jelly beans + 9 lb almonds cost $46. What is the cost per pound of each?

Let j = jelly-bean price, a = almond price. 5j + 3a = 20 and 7j + 9a = 46. Solving gives j = $1.75 per lb, a = $3.75 per lb.

Factor completely: x² − 11xy + 24y².

(x − 3y)(x − 8y).

Factor completely: 10y² + 17y − 20.

(2y