Algebra: Linear Equations/Inequalities Flashcards

Solve: |x − 3| = 7

Answer: x = 10 or x = −4

The absolute value equation gives x − 3 = 7 (x = 10) or x − 3 = −7 (x = −4).

A bus travels at a constant speed. It covers 180 miles in 3 hours. Which equation gives the distance d after t hours?

Answer: d = 60t

Speed = 180 ÷ 3 = 60 mph, so the linear equation is d = 60t.

For which value of k does the equation 3x + k = 3x − 5 have no solution?

Answer: Any k ≠ −5

Subtracting 3x gives k = −5; this is only true when k = −5, so any other value of k makes it a contradiction with no solution.

A student scored 78, 85, and 91 on three tests. What score s on the fourth test gives an average of at least 85?

Answer: s ≥ 86

Set up (78 + 85 + 91 + s)/4 ≥ 85; the sum is 254 + s ≥ 340, so s ≥ 86.

What is the solution to the system of equations if they graph as two parallel lines?

Answer: No solution

Parallel lines never intersect, so the system has no solution.

Solve for y: (2y + 6)/4 = 5

Answer: y = 7

Multiply both sides by 4: 2y + 6 = 20; subtract 6: 2y = 14; divide by 2: y = 7.

Which inequality is equivalent to −4x + 3 > 15?

Answer: x < −3

Subtract 3: −4x > 12; divide by −4 and flip the sign: x < −3.