Math / Algebra

QuestionSolve the equation: $4(x-2)=12$

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes the equation $4(x-2) = 12$ true. Watch out! Don't forget to apply the distributive property correctly and keep track of your signs!

STEP 2

1. Simplify the equation.
2. Isolate the term with $x$ .
3. Solve for $x$ .

STEP 3

Alright, let's kick things off by distributing the $4$ to both terms inside the parentheses.
Remember, this means multiplying both $x$ and $-2$ by $4$ .
So, $4 \cdot (x-2)$ becomes $4 \cdot x - 4 \cdot 2$ , which simplifies to $4x - 8$ .
Our equation now looks like this: $4x - 8 = 12$ .

STEP 4

To get $x$ by itself, we need to move that $-8$ to the other side of the equation.
The opposite of subtracting $8$ is adding $8$ , so let's add $8$ to both sides of the equation: $4x - 8 + 8 = 12 + 8$ .
This simplifies to $4x = \mathbf{20}$ .

STEP 5

Almost there!
We have $4x = 20$ , but we want just $x$ .
Since $x$ is being multiplied by $4$ , we'll divide both sides of the equation by $4$ to get $x$ all alone.
So, we have $\frac{4x}{4} = \frac{20}{4}$ .
This simplifies to $x = \mathbf{5}$ .

STEP 6

We found that $x = \mathbf{5}$ makes our original equation true.
So, our final answer is $x = 5$ !

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QuestionSolve the equation: $4(x-2)=12$

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes the equation $4(x-2) = 12$ true. Watch out! Don't forget to apply the distributive property correctly and keep track of your signs!

STEP 2

1. Simplify the equation.
2. Isolate the term with $x$ .
3. Solve for $x$ .

STEP 3

Alright, let's kick things off by distributing the $4$ to both terms inside the parentheses.
Remember, this means multiplying both $x$ and $-2$ by $4$ .
So, $4 \cdot (x-2)$ becomes $4 \cdot x - 4 \cdot 2$ , which simplifies to $4x - 8$ .
Our equation now looks like this: $4x - 8 = 12$ .

STEP 4

To get $x$ by itself, we need to move that $-8$ to the other side of the equation.
The opposite of subtracting $8$ is adding $8$ , so let's add $8$ to both sides of the equation: $4x - 8 + 8 = 12 + 8$ .
This simplifies to $4x = \mathbf{20}$ .

STEP 5

Almost there!
We have $4x = 20$ , but we want just $x$ .
Since $x$ is being multiplied by $4$ , we'll divide both sides of the equation by $4$ to get $x$ all alone.
So, we have $\frac{4x}{4} = \frac{20}{4}$ .
This simplifies to $x = \mathbf{5}$ .

STEP 6

We found that $x = \mathbf{5}$ makes our original equation true.
So, our final answer is $x = 5$ !

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QuestionSolve the equation: 4(x−2)=124(x-2)=124(x−2)=12

Studdy Solution

STEP 1

What is this asking? We need to find the value of xxx that makes the equation 4(x−2)=124(x-2) = 124(x−2)=12 true. Watch out! Don't forget to apply the distributive property correctly and keep track of your signs!

STEP 2

1. Simplify the equation.2. Isolate the term with xxx.3. Solve for xxx.

STEP 3

STEP 4

To get xxx by itself, we need to move that −8-8−8 to the other side of the equation.The opposite of subtracting 888 is adding 888, so let's **add** 888 to **both sides** of the equation: 4x−8+8=12+84x - 8 + 8 = 12 + 84x−8+8=12+8.This simplifies to 4x=204x = \mathbf{20}4x=20.

STEP 5

Almost there!We have 4x=204x = 204x=20, but we want just xxx.Since xxx is being multiplied by 444, we'll **divide both sides** of the equation by 444 to get xxx all alone.So, we have 4x4=204\frac{4x}{4} = \frac{20}{4}44x​=420​.This simplifies to x=5x = \mathbf{5}x=5.

STEP 6

We found that x=5x = \mathbf{5}x=5 makes our original equation true.So, our **final answer** is x=5x = 5x=5!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the equation: $4(x-2)=12$

What is this asking? We need to find the value of $x$ that makes the equation $4(x-2) = 12$ true. Watch out! Don't forget to apply the distributive property correctly and keep track of your signs!

1. Simplify the equation.
2. Isolate the term with $x$ .
3. Solve for $x$ .

To get $x$ by itself, we need to move that $-8$ to the other side of the equation.
The opposite of subtracting $8$ is adding $8$ , so let's add $8$ to both sides of the equation: $4x - 8 + 8 = 12 + 8$ .
This simplifies to $4x = \mathbf{20}$ .

Almost there!
We have $4x = 20$ , but we want just $x$ .
Since $x$ is being multiplied by $4$ , we'll divide both sides of the equation by $4$ to get $x$ all alone.
So, we have $\frac{4x}{4} = \frac{20}{4}$ .
This simplifies to $x = \mathbf{5}$ .

We found that $x = \mathbf{5}$ makes our original equation true.
So, our final answer is $x = 5$ !