Math / Algebra

QuestionQuestion 12
Complete each sentence to simplify the expression $(-4 t-7)+(3 t+8)$ . a. $-4 t$ and $3 t$ have a sum of Select Choice $\square$ b. -7 and 8 have a sum of Select Choice $\square$ c. The expression written in simplified form is Select Choice $\square$ (D) Need help with this question?

Studdy Solution

STEP 1

What is this asking? We're asked to simplify an expression by combining like terms, and explain how we did it step by step. Watch out! Be careful with the signs when combining terms.
A negative plus a negative is still negative, but a negative plus a positive... well, that depends on which one is bigger!

STEP 2

1. Combine the t terms.
2. Combine the constant terms.
3. Write the simplified expression.

STEP 3

Alright, let's wrangle those t terms!
We've got $-4t$ and $3t$ .
Remember, when we add, the order doesn't matter!
So, we can rewrite this as $3t + (-4t)$ or $3t - 4t$ .

STEP 4

Think of it like this: You gain 3 t's, but then you lose 4 t's.
What's the overall change?
You've lost 1 t!
So, $3t - 4t = -1t$ , which we can write more simply as $-t$ .

STEP 5

Now, let's tackle the numbers without any t's attached.
We have $-7$ and $8$ .
Again, order doesn't matter with addition, so we can rewrite this as $8 + (-7)$ or $8 - 7$ .

STEP 6

This one's straightforward! $8 - 7 = 1$ .
So, our constant term is just 1.

STEP 7

We found that the t terms combine to $-t$ and the constant terms combine to $1$ .

STEP 8

Putting it all together, our simplified expression is $-t + 1$ .
Boom!

STEP 9

a. $-4t$ and $3t$ have a sum of $-t$ . b. $-7$ and $8$ have a sum of $1$ . c. The expression written in simplified form is $-t + 1$ .

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Studdy Solution

STEP 1

STEP 2

1. Combine the t terms.
2. Combine the constant terms.
3. Write the simplified expression.

STEP 3

Alright, let's wrangle those t terms!
We've got $-4t$ and $3t$ .
Remember, when we add, the order doesn't matter!
So, we can rewrite this as $3t + (-4t)$ or $3t - 4t$ .

STEP 4

Think of it like this: You gain 3 t's, but then you lose 4 t's.
What's the overall change?
You've lost 1 t!
So, $3t - 4t = -1t$ , which we can write more simply as $-t$ .

STEP 5

Now, let's tackle the numbers without any t's attached.
We have $-7$ and $8$ .
Again, order doesn't matter with addition, so we can rewrite this as $8 + (-7)$ or $8 - 7$ .

STEP 6

This one's straightforward! $8 - 7 = 1$ .
So, our constant term is just 1.

STEP 7

We found that the t terms combine to $-t$ and the constant terms combine to $1$ .

STEP 8

Putting it all together, our simplified expression is $-t + 1$ .
Boom!

STEP 9

a. $-4t$ and $3t$ have a sum of $-t$ . b. $-7$ and $8$ have a sum of $1$ . c. The expression written in simplified form is $-t + 1$ .

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Studdy Solution

STEP 1

STEP 2

1. Combine the *t* terms.2. Combine the constant terms.3. Write the simplified expression.

STEP 3

Alright, let's **wrangle** those *t* terms!We've got −4t-4t−4t and 3t3t3t.Remember, when we add, the order doesn't matter!So, we can rewrite this as 3t+(−4t)3t + (-4t)3t+(−4t) or 3t−4t3t - 4t3t−4t.

STEP 4

Think of it like this: You *gain* 3 *t*'s, but then you *lose* 4 *t*'s.What's the overall change?You've *lost* 1 *t*!So, 3t−4t=−1t3t - 4t = -1t3t−4t=−1t, which we can write more simply as −t-t−t.

STEP 5

Now, let's **tackle** the numbers without any *t*'s attached.We have −7-7−7 and 888.Again, order doesn't matter with addition, so we can rewrite this as 8+(−7)8 + (-7)8+(−7) or 8−78 - 78−7.

STEP 6

This one's straightforward! 8−7=18 - 7 = 18−7=1.So, our constant term is just **1**.

STEP 7

We found that the *t* terms combine to −t-t−t and the constant terms combine to 111.

STEP 8

Putting it all together, our **simplified expression** is −t+1-t + 1−t+1.Boom!

STEP 9

a. −4t-4t−4t and 3t3t3t have a sum of −t-t−t. b. −7-7−7 and 888 have a sum of 111. c. The expression written in simplified form is −t+1-t + 1−t+1.

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1. Combine the t terms.
2. Combine the constant terms.
3. Write the simplified expression.

Alright, let's wrangle those t terms!
We've got $-4t$ and $3t$ .
Remember, when we add, the order doesn't matter!
So, we can rewrite this as $3t + (-4t)$ or $3t - 4t$ .

Think of it like this: You gain 3 t's, but then you lose 4 t's.
What's the overall change?
You've lost 1 t!
So, $3t - 4t = -1t$ , which we can write more simply as $-t$ .

Now, let's tackle the numbers without any t's attached.
We have $-7$ and $8$ .
Again, order doesn't matter with addition, so we can rewrite this as $8 + (-7)$ or $8 - 7$ .

This one's straightforward! $8 - 7 = 1$ .
So, our constant term is just 1.

We found that the t terms combine to $-t$ and the constant terms combine to $1$ .

Putting it all together, our simplified expression is $-t + 1$ .
Boom!

a. $-4t$ and $3t$ have a sum of $-t$ . b. $-7$ and $8$ have a sum of $1$ . c. The expression written in simplified form is $-t + 1$ .