One variable both sides word problems

Multiple Choice

• 3
• 1
• 2
• -2

Multiple Choice

Jacob solved the following equation using the steps shown.

Step 1 5x + 9 = 2x - 3

Step 2 3x + 9 = -3

Step 3 3x = -12

Step 4 x = -4

What operation did he perform to get from Step 1 to Step 2?

• Subtracted 2x from both sides of the equation

• Subtracted 9 from both sides of the equation

• Multiplied both sides of the equation by 3

• Added -3 to both sides of the equation

Multiple Choice

Which situation best represents the following equation?

25 + .05x = 50 + .01x

• There are two cell phone companies that charge based on the number of minutes used each month, x. Cellular One charges $50 plus 5 cents per minute. Cellular Plus charges $25 plus 1 cent per minute. How many minutes can be used in one month to make the two companies charge the same amount?

• There are two cell phone companies that charge based on the number of minutes used each month, x. Cellular One charges $25 plus $5 per minute. Cellular Plus charges $50 plus $1 per minute. How many minutes can be used in one month to make the two companies charge the same amount?

• There are two cell phone companies that charge based on the number of minutes used each month, x. Cellular One charges $25 plus 5 cents per minute. Cellular Plus charges $50. How many minutes can be used in one month to make the two companies charge the same amount?

• There are two cell phone companies that charge based on the number of minutes used each month, x. Cellular One charges $25 plus 5 cents per minute. Cellular Plus charges $50 plus 1 cent per minute. How many minutes can be used in one month to make the two companies charge the same amount?

Multiple Choice

• 3
• -2
• -3
• 4

No solutions or Infinitely Many Solutions

• No solutions - when you solve the equation your answer will not be true. For example : 2 = 8 is not a true statement so there is no solutions.

• Infinitely Many Solutions - when you solve the equation your answer will be a true statement. For example : 7 = 7 is a true statement so there is infinitely many solutions

Multiple Choice

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?

• 2 hours
• 3 hours
• 4 hours
• 5 hours

Match

Match the following

• Area of a Rectangle-

• Circumference given Diameter-

• Circumference given Radius-

• Perimeter of a Triangle-

• Volume of a Square-

a= L * W

C= pi D

C= 2 pi R

P= A+B+C

V= W * L * H

• a= L * W

• C= pi D

• C= 2 pi R

• P= A+B+C

• V= W * L * H

Multiple Choice

Which inequality can be represented by the inequality 20x + 50 < 25x

• Greg has $50 in his savings account. He deposits $20 in the account each week. His sister, Lauren opened an account today and will deposit $25 in the account each week. How many weeks will it take for Greg to have more money saved than Lauren?

• Greg has $50 in his savings account. He deposits $20 in the account each week. His sister, Lauren opened an account today and will put $25 in the account each week. How many weeks will it take for Lauren to have more money saved than Greg?

• Greg saves $20 each week to put in his savings account at the bank. His sister, Lauren has saved $50 and will save $25 each week. How many weeks will it take for Greg to have more money than Lauren?

• Greg has saved $50 and plans to put $25 each week in his savings account at the bank. His sister, Lauren has also saved $50 but will put $20 in her bank account each week.

Multiple Choice

Is 7 a solution to the equation?

3x+8-x = 5x-4

• yes

• maybe

• no

Dropdown

The Perimeter of any Triangle is the ​

Select answer

of its sides - ​

Select answer

Multiple Select

Check all steps that you would need to take to solve this equation:

$$4x-2=-2x+16$$  

• Use distributive property to get rid of parentheses

• Combine like terms

• Move the variable to one side of the equation

• Use inverse operations to isolate and solve for the variable.

Multiple Choice

The inequality shown below represents fees for two different apartments.

500x + 700 < 650x + 200

Which situation below does this inequality represent?

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is equal to Apartment A charging $650 per month with a $200 deposit.

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is greater than Apartment A charging $650 per month with a $200 deposit.

• Apartment A charges a $700 per month and then $500 deposit. Apartment B is greater than Apartment A charging $650 deposit with $200 per month.

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is less than Apartment A charging $650 per month with a $200 deposit.

Multiple Choice

Match the inequality to the word problem.Katie wants to have at least $200 in her bank account by the end of the month. She currently has $25 in her bank account. Katie makes $12 for each dog that she walks. How many dogs would Katie have to walk to reach her goal of $200?

• 25 - 12x ≥ 200
• 25 + 12x ≥ 200
• 13x ≥ 200
• 25 + 12x > 200

Multiple Select

Which of the equations shown below would be an example of a linear equation with a single variable? Remember that a linear equation with a single variable will not include any variables raised to a power or any roots of variables. These equations will also not include more than one variable, although the same variable can appear more than once. Check all that apply.

• $$a^2+25=50$$  

• $$4x-12=63$$  

• $$5\left(b-7\right)=8b+15$$  

• $$5c+d=45-a$$  

Multiple Choice

Select the situation that could be modeled by: 120 + 25x = 45x.

• John bought a car radio for $120 and speakers for $25 each. Joe bought a radio for $45. They each paid the same. How much did they spend?
• George charges a flat fee of $120 to mow a lawn plus $25 an hour. Greg charges $45 a hour to mow a lawn. After how many hours do they make the same amount?
• Lisa pays $120 for each purse she buys plus an additional $25 to have them personalized. Lauren pays $45 for each purse she buys. How many purses must they buy for the amount they spent to be the same?

Multiple Choice

What is the most important rule when solving equations?

• Always wash your hands.

• Whatever you do to one side of the equal sign, you have to do to the other.

• Pick the answer at random.

• Wait at least one hour after you eat.

Multiple Choice

Select the situation that could be modeled by: 8 + 4x = 12 + 3x.

• Winnie bought a family meal with 8 burgers and 4 fries. Wilson bought a family meal with 12 burgers and 3 fries. If they each paid the same amount, how much did they spend?
• Team A runs 8 drills that a 4 minutes each. Team B runs 12 drills that are 3 minutes each. Which team practices longer?
• The basketball team currently has 8 players and is growing by 4 players each month. The volleyball team has 12 players and is growing by 3 players each month. After how many months will they have the same number of players?

Multiple Choice

Select the situation that could be modeled by: 8 + 4x = 12 + 3x.

• Winnie bought a family meal with 8 burgers and 4 fries. Wilson bought a family meal with 12 burgers and 3 fries. If they each paid the same amount, how much did they spend?
• Team A runs 8 drills that a 4 minutes each. Team B runs 12 drills that are 3 minutes each. Which team practices longer?
• The basketball team currently has 8 players and is growing by 4 players each month. The volleyball team has 12 players and is growing by 3 players each month. After how many months will they have the same number of players?

Multiple Choice

Which inequality can be represented by the inequality 20x + 50 < 25x

• Greg has $50 in his savings account. He deposits $20 in the account each week. His sister, Lauren opened an account today and will deposit $25 in the account each week. How many weeks will it take for Greg to have more money saved than Lauren?

• Greg has $50 in his savings account. He deposits $20 in the account each week. His sister, Lauren opened an account today and will put $25 in the account each week. How many weeks will it take for Lauren to have more money saved than Greg?

• Greg saves $20 each week to put in his savings account at the bank. His sister, Lauren has saved $50 and will save $25 each week. How many weeks will it take for Greg to have more money than Lauren?

• Greg has saved $50 and plans to put $25 each week in his savings account at the bank. His sister, Lauren has also saved $50 but will put $20 in her bank account each week.

Multiple Choice

Mary has been offered two jobs. Job A has a starting salary of $36,000 and a raise of $1500 every year. Job B has a starting salary of $29,000 and a raise of $2500 every year. Write an equation to determine how many years would Mary's salary be the same at both companies. 

• 36,000x + 1,500 = 29,000x + 2,500
• 36,000 - 29,000 = 1,500x + 2,500x
• 36,000 - 1,500x = 29,000 - 2,500x
• 36,000 + 1,500x = 29,000 + 2,500x

Multiple Choice

Which situation best represents the following equation?

8.50x > 1000 + 2.50x

• Jose owns the local Comic Store. He sells comics for $8.50 each. His cost each month is $1,000 plus $2.50 per comic. How many comics, x, must he sell each month to make a profit?

• Jose owns the local Comic Store. He sells comics for $2.50 each. His cost each month is $1,000 plus $8.50 per comic. How many comics, x, must he sell each month to make a profit?

• Jose owns the local Comic Store. He sells comics for $2.50 each. His cost each month is $1,000 plus $2.50 per comic. How many comics, x, must he sell each month to make a profit?

• Jose owns the local Comic Store. He sells comics for $8.50 each. His cost each month is $1,000. How many comics, x, must he sell each month to make a profit?

Multiple Choice

Mike is driving a boat at 12 mph and is increasing his speed by 0.2 mph each second. Hank is driving a boat at 25 mph and is decreasing his speed by 0.7 mph each second. Which of the following equations could be used to determine x, the number of seconds it will take for the boats to be traveling the same speed?

• 12x + 0.2 = 25x - 0.7

• 12 - 0.2x = 25 + 0.7x

• 12.2x = -25.7x

• 12 + 0.2x = 25 - 0.7x

Multiple Choice

Renting games online from Netwii costs $3.33 per game  with no monthly fee.  Renting games online from HDO costs $2.00 per game plus a monthly fee of $10.00.
Which inequality represents the situation when the monthly cost at Netwii is more than the monthly cost at HDO?

• 3.33v > 2v + 10
• 3.33v + 10 > 2v 
• 3.33v < 2v + 10
• 3.33v + 10 < 2v

Multiple Choice

Sam make $10.25 per hour working at Cheddars.  He plans to buy a laptop for $550.  Write and solve an inequality describing how many hours h Sam will have to work to be able to buy the laptop. (Round to the next higher hour)

• 10.25h < 550; less than 54 hours
• 10.25h > 550; greater than 54 hours
• 10.25h ≤ 550; at most 54 hours
• 10.25h ≥ 550; at least 54 hours

Multiple Choice

The inequality shown below represents fees for two different apartments.

500x + 700 < 650x + 200

Which situation below does this inequality represent?

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is equal to Apartment A charging $650 per month with a $200 deposit.

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is greater than Apartment A charging $650 per month with a $200 deposit.

• Apartment A charges a $700 per month and then $500 deposit. Apartment B is greater than Apartment A charging $650 deposit with $200 per month.

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is less than Apartment A charging $650 per month with a $200 deposit.

Multiple Choice

Choose the situation that could represent the inequality:
25 – x < 15 + x

• Kasey has a gift card for $25. She buys a $15 CD and as many decals as she can buy with the rest of the gift card. How many decals can she buy?
• The school band has 25 people, and the theater class has 15 people. How many people must move from the band class to the theater class for the theater class to be as big or larger than the school band?