Question

Simplify to create an equivalent expression.5(10k + 1) + 2(2 + 8k)This is from khan academy I need a way to do the answer show work and give the answer

Answer 1

hello,

equivalent expressions are expressions which are equal to each other or the same with each other.

you can see them as mirror equations or expressions

to solve this expression, we to first simplfy the expression by opening the brackets and then adding the like terms.

step 1

open the bracket

`\begin{gathered} 9(10k\text{ }+\text{ 1})\text{ }+\text{ 2}(2+\text{ 8k}) \\ 90k\text{ }+\text{ 9 }+\text{ 4 }+\text{ 16k} \\ \text{add the variables and the numbers} \\ 106k\text{ }+\text{ 13} \end{gathered}`

step 2

now we've simplified the expression and we just need to find the equivalent expression for (106k + 13)

to do this, we just have to write an expression that it's exactly the same to (106k + 13)

-(-106k - 13) = 106k + 13

the equivalent expression for (106k + 13) is -(-106k - 13)