8th Grade Accelerated Algebra - 1st Semester Review

These flashcards cover a variety of algebraic concepts, including solving equations, inequalities, functions, and graphing.

What is the solution to the equation −5 + n/3 = 14?

n = 57.

How do you solve the equation −(3 − 5m) = 5(m − 3)?

m = 1.

What is the solution to the equation 8a − 9 = 3(3a + 2) + 5a?

a = 3.

What is the solution to the equation −3/4 x + 1/6 = 1/3 (−3/2 x + 1)?

x = 3.

Solve for |5x − 6| = 14.

x = 4 or x = −2.

What is the solution for −2|5 − 2w| = 14?

w = −2 or w = 9.

How do you solve for h in the equation V = 1/3Bh?

h = 3V/B.

How can you rearrange the equation y = 5x + dx − 3 to solve for x?

x = (y + 3 - dx)/5.

What inequality represents 'Two times the sum of a number and 6 is greater than or equal to 5'?

2(x + 6) ≥ 5.

What is the inequality representing 'Ten is at most a number minus 2'?

x - 2 ≤ 10.

Solve 8 + 10n > 2(7n − 1).

n < 1.

What is the solution to the inequality 15(1/3 x + 3) ≤ 6(x + 9)?

x ≥ -3.

Write an inequality for the area greater than 60 square feet for the rectangle with length x.

x > 60/width.

What is the solution to the compound inequality −2 ≤ 4 − 3x ≤ 13?

−3 ≤ x ≤ 5.

Solve 2y + 3 < 7 or −y + 9 ≤ 2.

y < 2 or y ≥ 7.

What is the solution for the compound inequality −8 < 1/2 (4x + 16) ≤ 10?

−1 < x ≤ 4.

What is the solution to the inequality 35 < 7(2 − x) or 1/4(20x − 16) ≥ 21?

x < −1 or x ≥ 5.

Solve the absolute value inequality −4|6d − 8| < 12.

−1 < 6d − 8 < 1.

What is the solution to 3|2x − 3| − 5 ≥ 16?

x ≤ −4 or x ≥ 7.

Do the points (5, 3), (3, 1), (1, −1), (3, −3), (5, −5) represent a function?

No, because the x-value 3 is repeated.

What is the domain and range in interval notation for the given points?

Domain: {1, 3, 5}; Range: {-5, -1, 1, 3}.

Determine if the function defined by (x, y) pairs is linear given the points (12, 17), (22, 13), (32, 9), (42, 5).

No, it is not linear.

What is the equation of a horizontal line?

y = c, where c is a constant.

What is the equation of a vertical line?

x = c, where c is a constant.

How do you find the x- and y-intercepts of −1/3x + 2y = −10?

x-intercept: (-30, 0), y-intercept: (0, -5).

What is the slope between the points (5, 7) and (−6, 2)?

Slope = -5/11.

Describe the transformations from f(x) = |x| to g(x) = −4/3|x − 3| − 1.

Reflect over x-axis, horizontal shrink by 3, right 3, down 1.

Write an absolute value function based on the transformation 'Horizontal shrink by 1/3, up 4.'

g(x) = |3x| + 4.

Write an absolute value function for 'Reflect over x-axis, left 3, down 2.'

g(x) = -|x + 3| - 2.