2.1 Solve Equations Using the Subtraction and Addition Properties of Equality

Checking whether a value is a solution, then isolating a variable by undoing addition or subtraction, including sentences translated from words.

Elementary Algebra 2e, 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality

Status

FlagsLoading your progress…

67 exercises

2.1 Exercise 1

Before you get started, take this readiness quiz.

Evaluate $x + 4$ when $x = −3$ .
If you missed this problem, review the reference.

2.5

2.1 Exercise 2

Evaluate $15 - y$ when $y = −5$ .
If you missed this problem, review the reference.

2.5

2.1 Exercise 3

Simplify $4 \left(4 n + 1\right) - 15 n$ .
If you missed this problem, review the reference.

2.5

2.1 Exercise 4

Translate into algebra “5 is less than $x$ .”
If you missed this problem, review the reference.

2.5

2.1 Exercise 6

Is $y = \frac{4}{3}$ a solution of $9 y + 2 = 6 y + 3$ ?

2.5

2.1 Exercise 7

Is $y = \frac{7}{5}$ a solution of $5 y + 3 = 10 y - 4$ ?

2.5

2.1 Exercise 9

Solve: $x + 19 = −27$ .

2.5

2.1 Exercise 10

Solve: $x + 16 = −34$ .

2.5

2.1 Exercise 12

Solve: $n - 61 = −75 .$

2.5

2.1 Exercise 13

Solve: $p - 41 = −73 .$

2.5

2.1 Exercise 15

Solve: $p - \frac{2}{3} = \frac{5}{6} .$

2.5

2.1 Exercise 16

Solve: $q - \frac{1}{2} = \frac{5}{6} .$

2.5

2.1 Exercise 18

Solve: $b - 0.47 = −2.1 .$

2.5

2.1 Exercise 19

Solve: $c - 0.93 = −4.6 .$

2.5

2.1 Exercise 21

Solve: $8 y - 4 - 7 y - 7 = 4 .$

2.5

2.1 Exercise 22

Solve: $6 z + 5 - 5 z - 4 = 3 .$

2.5

2.1 Exercise 24

Solve: $5 \left(p - 3\right) - 4 p = −10 .$

2.5

2.1 Exercise 25

Solve: $4 \left(q + 2\right) - 3 q = −8 .$

2.5

2.1 Exercise 27

Solve: $4 \left(2 h - 3\right) - 7 h = 6 \left(h - 2\right) - 6 \left(h - 1\right) .$

2.5

2.1 Exercise 28

Solve: $2 \left(5 x + 2\right) - 9 x = 3 \left(x - 2\right) - 3 \left(x - 4\right) .$

2.5

2.1 Exercise 30

Translate and solve: Ten more than x is equal to 41.

2.5

2.1 Exercise 31

Translate and solve: Twelve less than x is equal to 51.

2.5

2.1 Exercise 33

Translate and solve: The difference of $4 x$ and $3 x$ is 14.

2.5

2.1 Exercise 34

Translate and solve: The difference of $7 a$ and $6 a$ is $−8$ .

2.5

2.1 Exercise 36

Translate into an algebraic equation and solve:

The Pappas family has two cats, Zeus and Athena. Together, they weigh 23 pounds. Zeus weighs 16 pounds. How much does Athena weigh?

2.5

2.1 Exercise 37

Translate into an algebraic equation and solve:

Sam and Henry are roommates. Together, they have 68 books. Sam has 26 books. How many books does Henry have?

2.5

2.1 Exercise 38

Randell paid $28,675 for his new car. This was $875 less than the sticker price. What was the sticker price of the car?

2.5

2.1 Exercise 39

Translate into an algebraic equation and solve:

Eddie paid $19,875 for his new car. This was $1,025 less than the sticker price. What was the sticker price of the car?

2.5

2.1 Exercise 40

Translate into an algebraic equation and solve:

The admission price for the movies during the day is $7.75. This is $3.25 less the price at night. How much does the movie cost at night?

2.5

2.1 Exercise 41

Determine whether the given value is a solution to the equation.

Is $y = \frac{5}{3}$ a solution of
$6 y + 10 = 12 y$ ?

2.5

2.1 Exercise 43

Determine whether the given value is a solution to the equation.

Is $u = - \frac{1}{2}$ a solution of
$8 u - 1 = 6 u$ ?

2.5