Step: 1

Let x be the length of the original rope.

Step: 2

Length of each of the 7 pieces = x 7 ft

Step: 3

The variable expression for the new length of each piece is (x 7 - 2) ft.

[A length of 2 ft is cut from each of the 7 pieces.]

Correct Answer is : (x 7 - 2) ft

Step: 1

Let n be a number.

Step: 2

13 more than 8 times a number = 8n + 13.

[Write the expression.]

Step: 3

So, the variable expression for the phrase is 8n + 13.

Correct Answer is : 8n + 13

Step: 1

1 week = 7 days.

Step: 2

Number of days in n weeks = n × number of days in a week = n × 7 = 7n .

Step: 3

The variable expression for this situation is 7n .

Correct Answer is : 7n

Step: 1

Twice of an amount of juice will be equal to 2 × n or 2n .

Step: 2

One liter less than this amount will be equal to 2n - 1.

Step: 3

2n - 1 is the correct answer.

Correct Answer is : 2n - 1

Step: 1

Twice of an amount of sugar will be equal to 2 × n or 2n .

Step: 2

Ten grams less than this amount will be equal to 2n - 10.

Step: 3

2n -10 is the correct answer.

Correct Answer is : 2n - 10

Step: 1

Lindsay's present salary is $4y .

Step: 2

Lindsay's savings = $(4y - 1512)

[Savings = Income - Expenditure.]

Correct Answer is : $(4y - 1512)

Step: 1

Points scored by each person = Number of hits × p - Number of missed hits × q

Step: 2

Number of hits that Paul missed = (46 - 40) = 6

[Subtract.]

Step: 3

The variable expression for the points scored by Paul is 40p - 6q .

Step: 4

Number of hits that Matt missed = (46 - 38) = 8

[Subtract.]

Step: 5

The variable expression for the points scored by Matt is 38p - 8q .

Step: 6

So, the variable expressions for the points scored by Paul and Matt are 40p - 6q and 38p - 8q .

Correct Answer is : 40p - 6q , 38p - 8q

Step: 1

[In words.]

Step: 2

[Variable expression.]

Step: 3

Variable expression for the word phrase is y 38 .

Correct Answer is : y 3 8

Step: 1

5 times x = 5x

Step: 2

3 added to 5x = 3 + 5x

[Add 3 to 5x .]

Step: 3

3 added to 5 times x is equal to 19 is 3 + 5x = 19.

Correct Answer is : 3 + 5x = 19

Step: 1

Seven times the quantity of a number decreased by ten = 7(c - 10).

Step: 2

186 more than the number = 186 + c .

Step: 3

The algebraic sentence for the given word sentence: 7(c - 10) = 186 + c .

Correct Answer is : 7(c - 10) = 186 + c

Step: 1

4 times x = 4x

Step: 2

4 added to 4x = 4 + 4x

[Add 4 to 4x .]

Step: 3

4 added to 4 times x is equal to 19 is 4 + 4x = 19

Correct Answer is : 4 + 4x = 19

Step: 1

| w + 5 2 | - 4 > 5

Step: 2

| w + 5 2 | > 9

Step: 3

[Write the equivalent disjunction.]

Step: 4

(w + 5) > 18 or (w + 5) < -18

[Multiply throughout by 2.]

Step: 5

Step: 6

The solution set is {w : w < - 23 or w > 13}

Step: 7

The graphical representation is as follows:

Correct Answer is : Graph C

Step: 1

5 < | x - 4 |

Step: 2

5 < (x - 4) or - 5 > (x - 4)

[Write the equivalent disjunction.]

Step: 3

9 < x or - 1 > x

Step: 4

That is x < - 1 or x > 9

Step: 5

The solution set is {x : x < - 1 or x > 9}

Step: 6

The graphical representation is as follows:

Correct Answer is : Graph C

Step: 1

| 5 + 2(x - 1) | ≤1

Step: 2

5 + 2(x - 1) ≤ 1 and 5 + 2(x -1) ≥ - 1

Step: 3

2(x - 1) ≤- 4 and 2(x - 1) ≥ - 6

[Subtracting 5 from the two sides of the equation.]

Step: 4

(x - 1) ≤- 2 and (x - 1) ≥ - 3

[Divide throughout by 2.]

Step: 5

[Add 1 to both sides of the equation.]

Step: 6

The solution set is {x : - 2 ≤ x ≤- 1}

Step: 7

Correct Answer is : Graph B

Step: 1

The graph shows the values between - 3 and 1 including the points
-3, 1.

Step: 2

-3 ≤ x ≤ 1

Step: 3

-2 ≤ x + 1 ≤ 2

[Add 1 throughout.]

Step: 4

| x + 1 | ≤ 2

Correct Answer is : | x + 1 | ≤ 2

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