unit test 88%

Johan found that the equation -2|8 - x| - 6 = -12 had two possible solutions: x = 5 and x = -11. Which explains whether his solutions are correct?

He is not correct because he made a sign error.

Fiona solved the equation shown. 1/2 - 1/3(6x - 3) = -13/2 What is the missing step of her solution?

Simplify by combining like terms.

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

line 4

The tables represent the functions f(x) and g(x). Which input value produces the same output value for the two functions?

x = 1

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

x = 3

Solve the equation. -9x + 1 = -x + 17

x = -2

What is the value of x in the equation 2.5(6x - 4) = 10 + 4(1.5 + 0.5x)?

2

In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours or after working more than 9 hours. How can this be written as a single compound inequality?

h < 7 or h > 9

Kate begins solving the equation 2/3(6x - 3) = 1/2(6x - 4). Her work is correct and is shown below. 2/3(6x - 3) = 1/2(6x - 4) 4x - 2 = 3x - 2 When she adds 2 to both sides, the equation 4x = 3x results. Which is the best interpretation of this equation?

The equation has one solution: x = 0.

The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation |x - 72.5| = 4. What are the minimum and maximum temperatures in the house?

68.5°F and 76.5°F

Which situation could be represented by the graph?

Students in the children's choir are at least 8 years old but no more than 11 years old.

Deepak wrote out the steps to his solution of the equation 5/2 - 3x - 5 + 4x = -7/4 Which step has an incorrect instruction?

Step 1

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

k = 0.5

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

x ≥ 0.5

Solve the equation. y + 3 = -y + 9

y = 3

The inequality graphed below represents the ages, a, of players on a baseball team. Which inequality represents the same ages?

12 ≤ a < 18

Lily begins solving the equation 4(x - 1) - x = 3(x + 5) - 11. Her work is shown below. 4(x - 1) - x = 3(x + 5) - 11 4x - 4 - x = 3x + 15 - 11 3x - 4 = 3x + 4 How can her partial solution be interpreted?

The equation has no solution.

What is the value of n in the equation 1/2(n - 4) - 3 = 3 - (2n + 3)?

n = 2

What is the solution to the linear equation? 2/5 + p = 4/5 + 3/5p

p = 1

In order to be invited to tutoring or extension activities, a student's performance must be at least 20 points higher or lower than an average score. If the average score is 105, which inequality represents p, the scores for students who are eligible for tutoring or extension activities?

p ≤ 85 or p ≥ 125

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 - 45| = 3; minimum angle: 42 degrees

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

-12 + 20x ≥ -6x + 9

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

2

Step 1: -10 + 8x < 6x - 4 Step 2: -10 < -2x - 4 Step 3: -6 < -2x Step 4: ________ What is the final step in solving the inequality -2(5 - 4x) < 6x - 4?

x > 3

A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can't quite remember which. Either way, he is planning to pay her back or ask that she pay him back this afternoon. If he has $42.80 in his wallet, which equation represents the amount of money he may have after he sees Rita?

|x - 42.80| = 12