Answers Common Core Algebra I A-ICSolving One-Variable Inequalities

Solving One-Variable Inequalities — Unit test Answers

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What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

–12 – 20x ≤ –6x + 9

–12 – 20x ≥ –6x + 9

–12 + 20x ≤ –6x + 9

–12 + 20x ≥ –6x + 9

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Solve the inequality.2(4x – 3) ≥ –3(3x) + 5x?

x ≥ 0.5

x ≥ 2

(–∞, 0.5]

(–∞, 2]

The formula to convert °F to °C is C = (F – 32).Convert 50°C to °F.

10°F

20°F

122°F

132°F

Kate begins solving the equation (6x – 3) = (6x – 4). Her work is correct and is shown below.(6x – 3) = (6x – 4)4x – 2 = 3x – 2

The equation has infinite solutions.

The equation has one solution: x = 0.

The equation has one solution: x = .

The equation has no solution.

What is the value of n in the equation ?

n = 0

n = 2

n = 4

n = 6

Solve the inequality.2(4x – 3) ≥ –3(3x) + 5x?

x ≥ 0.5

x ≥ 2

(–∞, 0.5]

(–∞, 2]

Which input value produces the same output value for the two functions on the graph?

x = –3

x = –1

x = 1

x = 3

What is the value of n in the equation ?

n = 0

n = 2

n = 4

n = 6

The tables represent the functions f(x) and g(x).

x = –3

x = –1

x = 0

x = 1

What is the solution to the linear equation? + p = + p

p = 1

p = 2

p = 8

p = 10

Kate begins solving the equation (6x – 3) = (6x – 4). Her work is correct and is shown below.(6x – 3) = (6x – 4)4x – 2 = 3x – 2

The equation has infinite solutions.

The equation has one solution: x = 0.

The equation has one solution: x = .

The equation has no solution.

What is the solution to the linear equation?6k + 10.5 = 3k + 12

k = 0.5

k = 2

k = 7.3

k = 9

Simplify the expression shown.3x + 2 – 3x + 7 +5xWhat is the coefficient in the simplified expression?

The volume, V, of a rectangular prism is determined using the formula V=lwh, where l is the length, w is the width, and h is the height of the prism.Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches? Round to the nearest tenth.

0.2 inches

4.5 inches

46.1 inches

414.7 inches

The area, a, of an ellipse can be determined using the formula a = πxy, where x and y are half the lengths of the largest and smallest diameters of the ellipse.

y = a · πx

y = a + (πx)

y = a – πx

y = a ÷ (πx)

What value of x is in the solution set of 2x – 3 > 11 – 5x?

–3

Which number line represents the solutions to –2|x| = –6?

A number line from negative 8 to 8 in increments of 1. Two points, one at negative 6 and one at negative 2.

A number line from negative 8 to 8 in increments of 1. Two points, one at negative 8 and one at negative 4.

A number line from negative 8 to 8 in increments of 1. Two points, one at negative 4 and one at 4.

A number line from negative 8 to 8 in increments of 1. Two points, one at negative 3 and one at 3.

Solve the equation.–9x + 1 = –x + 17

x = –8

x = –2

x = 2

x = 8

Kari and Samantha have determined that their water-balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. Which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal?

|x – 3| = 45; minimum angle: 42 degrees

|x – 3| = 45; minimum angle: 45 degrees

|x – 45| = 3; minimum angle: 42 degrees

|x – 45| = 3; minimum angle: 45 degrees

Step 1: –10 + 8x < 6x – 4Step 2: –10 < –2x – 4Step 3: –6 < –2xStep 4: ________

x < –3

x > –3

x < 3

x > 3

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Solving One-Variable Inequalities — Unit test Answers

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