Question

Which expression is equivalent to 4 (3n - 5)?

Answer 1

Expression 4 (3n - 5) is equivalent to C: 12n - 20

Further explanation

Algebraic expressions in mathematics are a combination of coefficients, numbers, variables, constants and arithmetic operations such as addition, subtraction, multiplication, and division.

The main composition of algebraic expressions are:

• 1. phrases

algebraic forms separated by arithmetic operations

consists of one phrase (monomial) to many phrases (polynomial)

• 2. variable

is a value that can be changed, can be in the form of letters, for example, x, y, a, b, etc.

• 3. constants

is a fixed value, can be a number

• 4. arithmetic operations  ⇒ +, - , : , x

Calculation operations include multiply, divide, add, substract, etc.

There are several properties in integer multiplication operations

• 1. closed property

Multiplication between integers will produce integers too

• 2. commutative property

a x b = b x a

• 3. associative property

ax (bxc) = (axb) xc

• 4. identity

ax1 = 1 x a = a

• 5. distributive  property

* addition

ax (b + c) = axb + axc

* substraction

ax (b-c) = axb - axc

We can use distributive  property  of substraction   to solve the problem

$\displaystyle =4(3n-5)\\\\=4x3n - 4x5\\\\=12n-20$

"Equivalent to" means having the same value.

From the answer choices , which produce the same expression is C. 12n-20

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6 squared divided by 2 (3) +4

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an algebraic expression

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Keywords: PEMDAS, arithmetic operations, multiply, Parentheses, equivalent to

Answer 2

The expression that is equivalent to $4\left( {3n - 5} \right)$ is $\boxed{12n - 20}$. Option (C) is correct.

Further explanation:

To solve the grouping of multiplication, addition, subtraction and division always use the PEDMAS rule.

P represents the parenthesis, E represents exponents, M represents multiplication, D represents division, A represents addition and S represents subtraction.

Given:

The options are as follows,

A. $7\text{n} - 20$

B. $12\text{n} - 5$

C. $12\text{n} - 5$

D. $7\text{n} - 9$

Explanation:

The given expression is $4\left( {3n - 5} \right).$

Consider the expression as $\text{A}$.

$A = 4\left( {3n - 5} \right)$

Solve the expression $A = 4\left( {3n - 5} \right)$ to obtain the equivalent expression.

$\begin{aligned}A &= 4\left( {3n - 5} \right)\\&= 4 \times 3n - 4 \times 5\\&= 12n- 20\\\end{aligned}$

The expression that is equivalent to $4\left( {3n - 5} \right)$ is $\boxed{12n - 20}$. Option (C) is correct.

Option (A) is not correct.

Option (B) is not correct.

Option (C) is correct.

Option (D) is not correct.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: expression, equivalent, division, equation, multiplication, exponents, parenthesis.