Question

How do you simplify `28x+14+4x+16`? And if `x=4`, is the solution to both expressions the same?

Answer 1

`158`

Explanation:

First, you combine like terms so that would be `28x` and `4x` and `14` and `16`. Now we have the simplified expression

`32x + 30`

Then you would substitute `x = 4`, so now we have

`32(4) + 30`

If you multiply `32 xx 4` you get `128`, and now we have

`128 + 30 = 158`

Answer 2

Simplified, the expression is `32x+30`,

This is the same as `2 (16x + 15)`

If `x = 4`, both expressions are evaluated as `158`

Explanation:

Simplify    `28x + 14 + 4x + 16`

To simplify this expression, combine the like terms.

Sometimes it's easier to combine like terms if you collect them first by grouping them like with like.

1) Collect the like terms.
When you shuffle the terms around, you have to bring their signs with them.
`28x + 4x     +14 + 16`

2) Combine like terms
`32x + 30` `larr` answer

You can factor this expression if you want, but I don't know if you'd consider that more or less simplified
`2(16x + 15) larr` same answer

`color(white)(mmmmmmmm)`―――――――――

Let `x = 4` to check that the original expression comes out the same as the simplified expression.

If they don't come out the same, then there was a math mistake during the simplifying and the answer would be wrong.

Original expression
`28x + 14 + 4x + 16`    Let `x = 4`

1) Sub in `4` in the place of `x`
`28(4) + 14 + 4(4) + 16`

2) Clear the parentheses by multiplying
`112 + 14 + 16 + 16`

3) Combine like terms
`158` `larr` answer

`color(white)(mmmmmmmm)`―――――――――

Simplified expression
`32x + 30`

1) Sub in `4` in the place of `x`
`32(4) + 30`

2) Clear the parentheses
`128 + 30`

3) Combine like terms
`158` `larr` same answer

`color(white)(mmmmmmmm)`―――――――――

Factored expression
`2 (16x + 15)`

1) Sub in `4` in the place of `x`
`2 {16(4) + 15}`

2) Clear the inner parentheses
`2 (64 + 15)`

3) Combine like terms inside the parentheses
`2 (79)`

4) Clear the parentheses
`158` `larr` same answer