Equations in One Variable Assignment

For which equations is x = 9 a possible solution? Check all that apply.

|x| = 9 -|-x| = -9 |-x| = 9

The height of a triangle is 5 more than double the base length. If the height of the triangle is 74 mm, what is the base length of the triangle?

If b represents the length of the base in mm, the equation that represents this problem is 74 = 2b + 5 The base of the triangle is 34.5mm

It takes Mr. Martin 12 minutes to drive his bus route without stopping to pick up any passengers. For each passenger stop, he estimates that 30 seconds is added to his travel time. On Tuesday, Mr. Martin spends 14 minutes driving his route. Which equation can be used to determine the number of passenger stops, p, Mr. Martin had on Tuesday?

14 = 0.5p + 12

Mr. Vazquez determines that the area of a bathroom in his house is 25 square feet less than 1/5 of the area of the living room. If the bathroom measures 35 square feet, what is the area of the living room?

300 square feet

A family pays $8.00 to park at a concert. Tickets for the concert cost $13.50 per person. The family spent a total of $89.00 for parking fees and tickets to the concert. The situation can be modeled by the equation 89 = 13.5n + 8, where n represents the number of tickets purchased. How many concert tickets did the family purchase?

6 tickets

Jen solved the equation to determine the number of questions, x, she answered incorrectly on a test. She began by subtracting 100 from both sides, then multiplying both sides by -2. Which best describes the accuracy of Jen's work?

Correct. She could have also subtracted 100 from both sides, then divided by .

Study the steps used to solve the equation. Given: Step 1:c/2 - 5=7 Step 2:c/2 - 5+5=7+5 Step 3:c/2 + 0 = 12 Step 4:2(c/2 ) = 12(2) Step 5:c=24 Choose the property that justifies each step of the solution.

Step 1: addition property of equality Step 2: additive inverses Step 3: additive identity Step 4: multiplication property of equality

Analyze the solution shown. 1. -|-x| = 7: given 2. |-x| = -7: multiplication property of equality 3. -x = 7 or -x = -7: definition of absolute value 4. x = -7 or x = 7: multiplication property of equality 5. Check: -|-(-7)| = 7, -7 ≠ 7 -|-7| = 7, 7 = 7 Negative times negative is positive. Determine the flaws in the solution.

The definition of absolute value is applied incorrectly. There is no solution. In evaluating the solutions, the absolute value should be simplified first to get a positive value.

What is the solution set of -|-x| = -12?

{-12, 12}

Avni designs a game in which a player either wins or loses 4 points during each turn. Which equation represents all numbers of points, p, a player may have after his or her first turn of the game?

|p| = 4