Algebra, NAPX-E4-NC23

Question

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Worked Solution

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Variant 0

DifficultyLevel

685

Question

A positive number x\large x is multiplied by 6, then 12 is added.

Which of the following operations give the same result?

Worked Solution

Number = 6x6\large x + 12

Consider each option:

(x(\large x + 2) × 12 = 12x\large x + 24

(x(\large x + 2) × 6 = 6x\large x + 12   ✓\ \ \checkmark

(x(\large x + 6) × 2 = 2x\large x + 12

(x(\large x + 12) × 6 = 6x\large x + 72


∴\therefore Add 2 to x\large x, then multiply by 6.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A positive number $\large x$ is multiplied by 6, then 12 is added. Which of the following operations give the same result?
workedSolution
Number = $6\large x$ + 12 Consider each option: >>$(\large x$ + 2) × 12 = 12$\large x$ + 24 >>$(\large x$ + 2) × 6 = 6$\large x$ + 12 $\ \ \checkmark$ >>$(\large x$ + 6) × 2 = 2$\large x$ + 12 >>$(\large x$ + 12) × 6 = 6$\large x$ + 72
$\therefore$ Add 2 to $\large x$, then multiply by 6.
correctAnswer
Add 2 to $\large x$, then multiply by 6

Answers

Is Correct?Answer
x

Add 2 to x\large x, then multiply by 12.

✓

Add 2 to x\large x, then multiply by 6

x

Add 6 to x\large x, then multiply by 2.

x

Add 12 to x\large x, then multiply by 6.

Variant 1

DifficultyLevel

685

Question

A positive number x\large x is multiplied by 5, then 10 is added.

Which of the following operations give the same result?

Worked Solution

Number = 5x5\large x + 10

Consider each option:

(x(\large x + 2) × 5 = 5x\large x + 10   ✓\ \ \checkmark

(x(\large x + 5) × 2 = 2x\large x + 10

(x(\large x + 10) × 5 = 5x\large x + 50

(x(\large x + 3) × 2 = 2x\large x + 6


∴\therefore Add 2 to x\large x, then multiply by 5.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A positive number $\large x$ is multiplied by 5, then 10 is added. Which of the following operations give the same result?
workedSolution
Number = $5\large x$ + 10 Consider each option: >>$(\large x$ + 2) × 5 = 5$\large x$ + 10 $\ \ \checkmark$ >>$(\large x$ + 5) × 2 = 2$\large x$ + 10 >>$(\large x$ + 10) × 5 = 5$\large x$ + 50 >>$(\large x$ + 3) × 2 = 2$\large x$ + 6
$\therefore$ Add 2 to $\large x$, then multiply by 5.
correctAnswer
Add 2 to $\large x$, then multiply by 5

Answers

Is Correct?Answer
✓

Add 2 to x\large x, then multiply by 5

x

Add 5 to x\large x, then multiply by 2.

x

Add 10 to x\large x, then multiply by 5.

x

Add 3 to x\large x, then multiply by 2.

Variant 2

DifficultyLevel

681

Question

A positive number x\large x is multiplied by 3, then 6 is added.

Which of the following operations give the same result?

Worked Solution

Number = 3x3\large x + 6

Consider each option:

(x(\large x + 3) × 2 = 2x\large x + 6

(x(\large x + 6) × 3 = 6x\large x + 18

(x(\large x + 2) × 3 = 3x\large x + 6   ✓\ \ \checkmark

(x(\large x + 2) × 6 = 6x\large x + 12


∴\therefore Add 2 to x\large x, then multiply by 3.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A positive number $\large x$ is multiplied by 3, then 6 is added. Which of the following operations give the same result?
workedSolution
Number = $3\large x$ + 6 Consider each option: >>$(\large x$ + 3) × 2 = 2$\large x$ + 6 >>$(\large x$ + 6) × 3 = 6$\large x$ + 18 >>$(\large x$ + 2) × 3 = 3$\large x$ + 6 $\ \ \checkmark$ >>$(\large x$ + 2) × 6 = 6$\large x$ + 12
$\therefore$ Add 2 to $\large x$, then multiply by 3.
correctAnswer
Add 2 to $\large x$, then multiply by 3

Answers

Is Correct?Answer
x

Add 3 to x\large x, then multiply by 2.

x

Add 6 to x\large x, then multiply by 3.

✓

Add 2 to x\large x, then multiply by 3

x

Add 2 to x\large x, then multiply by 6.

Variant 3

DifficultyLevel

686

Question

A positive number x\large x is multiplied by 4, then 8 is added.

Which of the following operations give the same result?

Worked Solution

Number = 4x4\large x + 8

Consider each option:

(x(\large x + 2) × 8 = 8x\large x + 16

(x(\large x + 8) × 2 = 2x\large x + 16

(x(\large x + 4) × 2 = 2x\large x + 8

(x(\large x + 2) × 4 = 4x\large x + 8   ✓\ \ \checkmark


∴\therefore Add 2 to x\large x, then multiply by 6.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A positive number $\large x$ is multiplied by 4, then 8 is added. Which of the following operations give the same result?
workedSolution
Number = $4\large x$ + 8 Consider each option: >>$(\large x$ + 2) × 8 = 8$\large x$ + 16 >>$(\large x$ + 8) × 2 = 2$\large x$ + 16 >>$(\large x$ + 4) × 2 = 2$\large x$ + 8 >>$(\large x$ + 2) × 4 = 4$\large x$ + 8 $\ \ \checkmark$
$\therefore$ Add 2 to $\large x$, then multiply by 6.
correctAnswer
Add 2 to $\large x$, then multiply by 4.

Answers

Is Correct?Answer
x

Add 2 to x\large x, then multiply by 8.

x

Add 8 to x\large x, then multiply by 2.

x

Add 4 to x\large x, then multiply by 2.

✓

Add 2 to x\large x, then multiply by 4.

Variant 4

DifficultyLevel

688

Question

A positive number x\large x is multiplied by 6, then 12 is subtracted.

Which of the following operations give the same result?

Worked Solution

Number = 6x6\large x −- 12

Consider each option:

(x(\large x −- 2) × 12 = 12x\large x −- 24

(x(\large x −- 2) × 6 = 6x\large x −- 12   ✓\ \ \checkmark

(x(\large x −- 6) × 2 = 2x\large x −- 12

(x(\large x −- 12) × 6 = 6x\large x −- 72


∴\therefore Subtract 2 from x\large x, then multiply by 6.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A positive number $\large x$ is multiplied by 6, then 12 is subtracted. Which of the following operations give the same result?
workedSolution
Number = $6\large x$ $-$ 12 Consider each option: >>$(\large x$ $-$ 2) × 12 = 12$\large x$ $-$ 24 >>$(\large x$ $-$ 2) × 6 = 6$\large x$ $-$ 12 $\ \ \checkmark$ >>$(\large x$ $-$ 6) × 2 = 2$\large x$ $-$ 12 >>$(\large x$ $-$ 12) × 6 = 6$\large x$ $-$ 72
$\therefore$ Subtract 2 from $\large x$, then multiply by 6.
correctAnswer
Subtract 2 from $\large x$, then multiply by 6

Answers

Is Correct?Answer
x

Subtract 2 from x\large x, then multiply by 12.

✓

Subtract 2 from x\large x, then multiply by 6

x

Subtract 6 from x\large x, then multiply by 2.

x

Subtract 12 from x\large x, then multiply by 6.

Variant 5

DifficultyLevel

688

Question

A positive number x\large x is multiplied by 5, then 10 is subtracted.

Which of the following operations give the same result?

Worked Solution

Number = 5x5\large x −- 10

Consider each option:

(x(\large x −- 2) × 5 = 5x\large x −- 10   ✓\ \ \checkmark

(x(\large x −- 5) × 2 = 2x\large x −- 10

(x(\large x −- 10) × 5 = 5x\large x −- 50

(x(\large x −- 5) × 5 = 5x\large x −- 25


∴\therefore Subtract 2 from x\large x, then multiply by 5.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A positive number $\large x$ is multiplied by 5, then 10 is subtracted. Which of the following operations give the same result?
workedSolution
Number = $5\large x$ $-$ 10 Consider each option: >>$(\large x$ $-$ 2) × 5 = 5$\large x$ $-$ 10 $\ \ \checkmark$ >>$(\large x$ $-$ 5) × 2 = 2$\large x$ $-$ 10 >>$(\large x$ $-$ 10) × 5 = 5$\large x$ $-$ 50 >>$(\large x$ $-$ 5) × 5 = 5$\large x$ $-$ 25
$\therefore$ Subtract 2 from $\large x$, then multiply by 5.
correctAnswer
Subtract 2 from $\large x$, then multiply by 5

Answers

Is Correct?Answer
✓

Subtract 2 from x\large x, then multiply by 5

x

Subtract 5 from x\large x, then multiply by 2.

x

Subtract 10 from x\large x, then multiply by 5.

x

Subtract 5 from x\large x, then multiply by 5.

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