Understanding linear equations in one variable

a number less than 22 is 47

• t - 22 = 47

• 22 - x = 47

• 47 - 22 = k

• m - 47 = 22

12 less than the quotient of a number and 3 is 24.

• (n ÷ 3) − 12 = 24
• 12 − (n ÷ 3) = 24
• (n ÷ 12) − 3 = 24
• 3 − (n ÷ 12) = 24

30% of the students surveyed said they had read at least one Harry Potter book. If 660 students answered that they had read a Harry Potter book, how many students were surveyed?

Translate the following sentence into an algebraic equation. Use the variable h to represent the height of the ladder.

The quotient of the ladder's height and 4 is 6.

• $\frac{4}{6}=x$

• $\frac{x}{4}=6$

• $\frac{4}{x}=6$

• $\frac{6}{4}=x$

The Johnson family wants to join a gym.  There is a fee of $125 to join plus $45 per month membership fee.  They budgeted $800 for the gym membership.  Which equation shows how many months will they be able to have a membership?

• 125 + 800x = 45
• 45x + 125 = 800
• 125x + 45 = 800
• 45x - 125 = 800

The product of a number g and 5 is 30

• g5 - 30

• g ÷ 5 = 30

• 5g= 30

Translate this verbal equation into an algebraic equation:

The product of 17 and the number, s, is 68

• 17/s = 68

• 17 + s = 68

• 17s = 68

• s - 17 = 68

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?

• 15x + 2.5 = 10x + 3

• 15 - 2.5x = 10 - 3x

• 15 + 2.5x = 10 + 3x

• 15 - 10 = 2.5x + 3x

Write the verbal sentence as an equation:

The difference of seven times a number and 15 is 41.

• 7 - n • 15 = 41

• (7 - n) • 15 = 41

• 7n + 15 = 41

• 7n - 15 = 41

Which problem situation matches the equation?

$3.25h + $12.50 = $45

• Jaime needs $12.50 to buy a video game. She has $3.25. She can earn $45 per hour doing chores.

• Jaime needs $45 to buy a video game. She has $12.50. She can earn $3.25 per hour doing chores.

• Jaime needs $3.25 to buy a video game. She has $12.50. She can earn $45 per hour doing chores.

• None of the above.