Linear Equations and Inequalities Flashcards

Two distinct lines are parallel if they have:

Answer: The same slope

Parallel lines never intersect and always have equal slopes but different y-intercepts.

Solve: (x + 3)/2 = 5

Answer: x = 7

Multiplying both sides by 2 gives x + 3 = 10, and subtracting 3 gives x = 7.

Find x: 4x + 2 = 2x + 10

Answer: x = 4

Subtracting 2x from both sides gives 2x + 2 = 10, then 2x = 8, so x = 4.

Solve: −2(x + 3) + 4 = −6

Answer: x = 2

Distributing gives −2x − 6 + 4 = −6, simplifying to −2x − 2 = −6, then −2x = −4, so x = 2.

What is the solution set of |x| = 5?

Answer: {5, −5}

The absolute value equation |x| = 5 is satisfied by both x = 5 and x = −5, since |5| = |−5| = 5.

A line has equation y = −x + 7. What is the slope?

Answer: −1

In y = mx + b, the coefficient of x is m = −1 (since −x = −1·x), which is the slope.

Which number line correctly shows the solution to x + 2 ≤ 6?

Answer: A closed circle at 4, shaded to the left

Subtracting 2 from both sides gives x ≤ 4; the closed circle includes 4, and shading left shows all values less than or equal to 4.