Question $(-4.3v + 3.4t) - (2.8v - 4.1t)$

Studdy Solution

STEP 1

What is this asking? Simplify the expression by combining like terms. Watch out! Be careful with the signs when subtracting!
It's easy to make a mistake there.

STEP 2

1. Distribute the negative sign
2. Group like terms
3. Combine like terms

STEP 3

Alright, let's kick things off by distributing the negative sign to the terms inside the second parentheses.
Remember, subtracting is the same as adding the opposite, so we're essentially multiplying each term in the second parentheses by $-1$ .
This is super important because it changes the signs of those terms!

STEP 4

$(-4.3v + 3.4t) + (-1)(2.8v - 4.1t)$ $(-4.3v + 3.4t) + (-1 \cdot 2.8v) + (-1 \cdot -4.1t)$ $-4.3v + 3.4t - 2.8v + 4.1t$

STEP 5

Now, let's group our like terms together.
This makes it way easier to see what we're combining.
We put the v terms together and the t terms together.
Think of it like sorting your socks – you want to match the similar ones!

STEP 6

$(-4.3v - 2.8v) + (3.4t + 4.1t)$

STEP 7

Time to combine those like terms!
We add the coefficients of the v terms together and the coefficients of the t terms together.

STEP 8

$(-4.3 - 2.8)v + (3.4 + 4.1)t$ $-7.1v + 7.5t$

STEP 9

Our final simplified expression is $-7.1v + 7.5t$ !

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