Solving One-Step Equations Adding & Subtracting

#6.1 Homework Practice

Solving One-Step Equations  Adding & Subtracting

1. Use the algebra tiles to solve the equation

1. A model for the equation is shown below.

1. What is the solution of this equation?

1. 564 C. 886
2. 554 D. 544

1. Solve the equation
   

1. Angela gave 23 books to her younger brother. She had 57 books left. You can solve the equation to find the number of books Angela had before she gave books to her brother. What is the solution to the equation?

1. 39 C. 70
2. 34 D. 80

#6.2 Homework Practice

Solving One-Step Equations  Multiplying & Dividing

1. Use the algebra tiles to solve the equation

1. Find the solution to the equation . Use the algebra tiles to help you.

1. Your school has a competition to see who can read the most book sin 126 days. Solve the equation to find w, the number of weeks in 126 days.

1. Which value of y makes this equation true?

1. 5 C. 108
2. 72 D. 25

1. Solve the equation for z.

#6.3 Homework Practice

Solving One-Step Equations with Rational Numbers

1. In a certain country, there are about 8.0 million people. Of those 1.6 million do not have access to safe drinking water. Solve the equation to find p, the number of people (in millions) who have access to safe drinking water.

1. Seth purchased several roses for a total of $11.25 and had $23.50 left over. Use the equation below to determine the amount of money Seth had before purchasing the roses.

1. $12.25 C. $34.75
2. $35.25 D. $33.75

1. What number goes into the box to make the equation true?

1. 0.22 C. 0.31
2. 0.12 D. 0.88

1. About of a certain planet’s surface is covered with either water or desert. About is covered with water. Solve the equation to find d , the part of the planet’s surface covered with desert.

1. Of the students in your class prefer apple juice. In total, of the students prefer apple juice or orange juice. Write an equation to find t, the fraction of students who prefer orange juice. Then solve the equation.

#6.4 Homework Practice

Solving One-Step Equations with Rational Numbers

1. A rover on a planet traveled about 1.2 kilometers during its first year exploring. Solve the equation to find the distance, d, in kilometers that the rover would travel at this rate in 2.1 years.

1. Solve the equation

1. A restaurant made a sandwich that had a length of 3.6 meters. The sandwich was then cut into equal lengths that were 0.15 meters each to make smaller sandwiches. Use the equation below to find x, the total number of smaller sandwiches made.

1. 76 C. 3
2. 15 D. 24

1. On a certain planet, objects weigh about of what they weigh on Earth. An object weighs pounds on the planet. Solve the equation for w to find the object’s weight on Earth, in pounds.

1. Tina and four friends each paid $105 for the camping trip. Tina used the equation below to calculate the total cost for the trip. What was the total cost of the trip?

1. $525 C. $425
2. $100 D. $21.00

#6.5 Homework Practice

Solving Two-Step Equations

1. You receive $121 in all for selling paintings. You cold one painting for $26 and the rest for $19 each. Solve the equation below to find x, the number of $19 paintings you sold.

1. Kathy is 32 years old. She is 4 years younger than 6 times her daughter’s age. The equation , where x equals her daughter’s age, can be used to find the age of Kathy’s daughter. How old is Kathy’s daughter?

1. 8 years old C. 4 years old
2. 7 years old D. 6 years old

1. A customer has $75 to spend on art supplies. With each $9 canvas, she buys a frame. She buys 5 canvas-frame combinations. Solve the equation below to find x, the number of dollars she can spend on each frame.

1. Use the form below. What is the value of x when p = 4, q = 7 and r = 32?

1. x = 0 C. x = 1
2. x = 2 D. x = 9

1. A rental car agency charges $220 per week plus $0.25 per mile to rend a car. Solve the equation below to find x, the number of miles you can travel in one week for $405.

#6.6 Homework Practice

Solving Two-Step Equations

1. Complete the steps to solve the equation

1. Solve the following equation

1. When seven times a number is decreased by 2, the result is 19.

1. In 2000, the number of federal hazardous waste sites in State X was 10 less than four times the number of sites in State Y. Suppose there were 62 such sites in State X. Solve the following equation to find the number of sites in State Y.

1. A student solved the equation using algebra tiles. He incorrectly says the solution is 7. What mistake might the student have made?

1. He divided each side by the 1’s instead of multiplying them.
2. He added the 1’s to the right side instead of subtracting them.
3. He multiplying each side by the 1’s instead of dividing by them.
4. He subtracted 1’s from the right side instead of adding them.

#6.7 Homework Practice

Writing Equations

1. Identify which of the following are equations. Check all that apply.

1. D.

1. E.

1. F.

1. Tim says that is an expression. James says that is an equation. Who is right?

1. Write an equation. 5 less than n is 3

1. C.
2. D.

1. Write an equation that represents this situation.

1. Kate has 64 marbles. Allison has 42 marbles more than Kate. Write an equation using m, to represent the number of marbles Allison has.

#6.8 Homework Practice

Writing Two-Step Equations

1. Last night, 6 friends went out to dinner at a restaurant. They split the bill evenly. Each friend paid $13.75. If B represents the total bill in dollars, what equation could you use to find the value of B? Write clue words in the box and show your translation.

1. A garden contains 110 flowers, each of which is either red or orange. There are 75 orange flowers. If R. represents the number of red flowers in the garden, which equation could you use to find the value of R? Write clue words in the box and show your translation.

1. C.

1. D.

1. At a graduation dinner, an equal number of guests was seated at each of 6 large tables, and 4 late-arriving guests were seated at a smaller table. There were 52 guests in all. If n represents the number of people at each large table, what equation could you use to find the value of n?

1. How would this equation be written in words?

1. Eleven less than eight times a number is 6.
2. Eight more than eleven times a number is 6.
3. Eight less than eleven times a number is 6.
4. Eleven more than eight times a number is 6.

1. Which equation can be represented by the following description.

#6.9 Homework Practice

Translating Inequalities

Circle the correct inequality based on the given situation:

1. Yolanda wants to score at least 84% on the next history test.

1. In NY, teens must be at least 16 years old to obtain a driver’s license.

1. Mike pays $30 for a ticket to an amusement park. He cannot spend more than $50. How much more than he spend at the park?

1. Kai has $4.99 left on a music download gift card. She has a download costing $1.99 in her online shopping cart. How much money does Kai have left to spend?

1. Write a real-world situation that could be represented by .

______

______

#6.10 Homework Practice

Translating Inequalities

Translate the following real-world situations using inequality symbols, then graph.

1. At most, I can spend $35 at the grocery story.

1. Kerry weighed less than 100 pounds in middle school.

1. The vet said my dog, Duke, should not be over 70 pounds.

Graph the following inequalities on number lines you create.