Math / Algebra

QuestionPre-Test Active 1 2 3 4 5
What is the simplified expression for the expression below? $-1(2 x+3)-2(x-1)$ $-4 x+1$ $-4 x-2$ $-4 x+2$ $-4 x-1$

Studdy Solution

STEP 1

What is this asking? We need to simplify the expression $-1(2x + 3) - 2(x - 1)$ by combining like terms. Watch out! Be super careful with those negative signs; they can be sneaky!
Don't forget to distribute them correctly.

STEP 2

1. Distribute the $-1$ .
2. Distribute the $-2$ .
3. Combine like terms.

STEP 3

Alright, let's kick things off by distributing the $-1$ across the terms inside the first parentheses, $(2x + 3)$ .
Remember, multiplying by $-1$ flips the sign of each term.

STEP 4

$-1 \cdot 2x + (-1) \cdot 3 = -2x - 3$ So, $-1(2x + 3)$ simplifies to $-2x - 3$ .

STEP 5

Now, let's tackle the second part of the expression.
We'll distribute the $-2$ across the terms inside the second parentheses, $(x - 1)$ .

STEP 6

$-2 \cdot x + (-2) \cdot (-1) = -2x + 2$ So, $-2(x - 1)$ simplifies to $-2x + 2$ .

STEP 7

Time to bring it all together! We've got $-2x - 3$ from the first part and $-2x + 2$ from the second part.
Let's combine the x terms and the constant terms separately.

STEP 8

$-2x - 3 - 2x + 2$ Combining the x terms: $-2x - 2x = -4x$ Combining the constant terms: $-3 + 2 = -1$

STEP 9

Putting it all together, we get: $-4x - 1$

STEP 10

The simplified expression is $-4x - 1$ .

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QuestionPre-Test Active 1 2 3 4 5
What is the simplified expression for the expression below? $-1(2 x+3)-2(x-1)$ $-4 x+1$ $-4 x-2$ $-4 x+2$ $-4 x-1$

Studdy Solution

STEP 1

What is this asking? We need to simplify the expression $-1(2x + 3) - 2(x - 1)$ by combining like terms. Watch out! Be super careful with those negative signs; they can be sneaky!
Don't forget to distribute them correctly.

STEP 2

1. Distribute the $-1$ .
2. Distribute the $-2$ .
3. Combine like terms.

STEP 3

Alright, let's kick things off by distributing the $-1$ across the terms inside the first parentheses, $(2x + 3)$ .
Remember, multiplying by $-1$ flips the sign of each term.

STEP 4

$-1 \cdot 2x + (-1) \cdot 3 = -2x - 3$ So, $-1(2x + 3)$ simplifies to $-2x - 3$ .

STEP 5

Now, let's tackle the second part of the expression.
We'll distribute the $-2$ across the terms inside the second parentheses, $(x - 1)$ .

STEP 6

$-2 \cdot x + (-2) \cdot (-1) = -2x + 2$ So, $-2(x - 1)$ simplifies to $-2x + 2$ .

STEP 7

Time to bring it all together! We've got $-2x - 3$ from the first part and $-2x + 2$ from the second part.
Let's combine the x terms and the constant terms separately.

STEP 8

$-2x - 3 - 2x + 2$ Combining the x terms: $-2x - 2x = -4x$ Combining the constant terms: $-3 + 2 = -1$

STEP 9

Putting it all together, we get: $-4x - 1$

STEP 10

The simplified expression is $-4x - 1$ .

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QuestionPre-Test Active 1 2 3 4 5What is the simplified expression for the expression below? −1(2x+3)−2(x−1)-1(2 x+3)-2(x-1)−1(2x+3)−2(x−1) −4x+1-4 x+1−4x+1 −4x−2-4 x-2−4x−2 −4x+2-4 x+2−4x+2 −4x−1-4 x-1−4x−1

Studdy Solution

STEP 1

What is this asking? We need to simplify the expression −1(2x+3)−2(x−1)-1(2x + 3) - 2(x - 1)−1(2x+3)−2(x−1) by combining like terms. Watch out! Be super careful with those negative signs; they can be sneaky!Don't forget to distribute them correctly.

STEP 2

1. Distribute the −1-1−1.2. Distribute the −2-2−2.3. Combine like terms.

STEP 3

Alright, let's **kick things off** by distributing the −1-1−1 across the terms inside the first parentheses, (2x+3)(2x + 3)(2x+3).Remember, multiplying by −1-1−1 flips the sign of each term.

STEP 4

−1⋅2x+(−1)⋅3=−2x−3-1 \cdot 2x + (-1) \cdot 3 = -2x - 3−1⋅2x+(−1)⋅3=−2x−3 So, −1(2x+3)-1(2x + 3)−1(2x+3) simplifies to −2x−3-2x - 3−2x−3.

STEP 5

Now, let's **tackle** the second part of the expression.We'll distribute the −2-2−2 across the terms inside the second parentheses, (x−1)(x - 1)(x−1).

STEP 6

−2⋅x+(−2)⋅(−1)=−2x+2-2 \cdot x + (-2) \cdot (-1) = -2x + 2−2⋅x+(−2)⋅(−1)=−2x+2 So, −2(x−1)-2(x - 1)−2(x−1) simplifies to −2x+2-2x + 2−2x+2.

STEP 7

**Time to bring it all together!** We've got −2x−3-2x - 3−2x−3 from the first part and −2x+2-2x + 2−2x+2 from the second part.Let's combine the *x* terms and the constant terms separately.

STEP 8

−2x−3−2x+2-2x - 3 - 2x + 2−2x−3−2x+2 Combining the *x* terms: −2x−2x=−4x-2x - 2x = -4x−2x−2x=−4x Combining the constant terms: −3+2=−1-3 + 2 = -1−3+2=−1

STEP 9

Putting it all together, we get: −4x−1-4x - 1−4x−1

STEP 10

The simplified expression is −4x−1-4x - 1−4x−1.

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QuestionPre-Test Active 1 2 3 4 5
What is the simplified expression for the expression below? $-1(2 x+3)-2(x-1)$ $-4 x+1$ $-4 x-2$ $-4 x+2$ $-4 x-1$

What is this asking? We need to simplify the expression $-1(2x + 3) - 2(x - 1)$ by combining like terms. Watch out! Be super careful with those negative signs; they can be sneaky!
Don't forget to distribute them correctly.

1. Distribute the $-1$ .
2. Distribute the $-2$ .
3. Combine like terms.

Alright, let's kick things off by distributing the $-1$ across the terms inside the first parentheses, $(2x + 3)$ .
Remember, multiplying by $-1$ flips the sign of each term.

$-1 \cdot 2x + (-1) \cdot 3 = -2x - 3$ So, $-1(2x + 3)$ simplifies to $-2x - 3$ .

Now, let's tackle the second part of the expression.
We'll distribute the $-2$ across the terms inside the second parentheses, $(x - 1)$ .

$-2 \cdot x + (-2) \cdot (-1) = -2x + 2$ So, $-2(x - 1)$ simplifies to $-2x + 2$ .

Time to bring it all together! We've got $-2x - 3$ from the first part and $-2x + 2$ from the second part.
Let's combine the x terms and the constant terms separately.

$-2x - 3 - 2x + 2$ Combining the x terms: $-2x - 2x = -4x$ Combining the constant terms: $-3 + 2 = -1$

Putting it all together, we get: $-4x - 1$

The simplified expression is $-4x - 1$ .