Question

Which expressions are equivalent to 6 + 12x?
Select each equivalent expression.

Answer 1

Equivalent expressions for 6 + 12x can be found through algebraic manipulations, such as the distributive property and multiplying by fractions that equal 1, ensuring that the simplified result still yields 6 + 12x.

Step-by-step explanation:

To find equivalent expressions for 6 + 12x, we need to use algebraic rules and properties such as the distributive property, combining like terms, and the multiplication of integers. Considering the information provided about the multiplication of signed numbers, we look for expressions that have the same combination of constants and coefficients in terms of x after following these algebraic rules. An expression like 3(2 + 4x) is equivalent after applying the distributive property, giving us 6 + 12x.

Another equivalent expression could be obtained by factoring out a common factor or by multiplying the whole expression by a fraction that equals 1, such as 2/2(6 + 12x), which simplifies back to 6 + 12x. It's important to simplify the expression and ensure that the result is reasonable through each step of the process. Incorrect operations or failure to correctly apply mathematical rules could result in nonequivalent expressions.

Answer 2

2 (3 + 6x), 3 (2 + 4x) and 6 (1 + 2x)

Step-by-step explanation:

Given the expression 6 + 12x.

The following functions are equivalent;

Factoring out common number;

For 2;

2(3) + 2(6x)

2 (3 + 6x)

Factoring out 3;

3(2) + 3(4x)

3 (2 + 4x)

Factoring out 6;

6(1) + 6(2x)

6 (1 + 2x)

Hence the possible equivalent expressions are 2 (3 + 6x), 3 (2 + 4x) and 6 (1 + 2x)