Question

consider this equation

4(3x - 2) = -24

determine the value of x

Answer 1

consider this equation

-2(4 + n) = 24

correctly order the steps used to solve this equation

Answer 2

what do you mean by distribute the -2

Answer 3

To solve the equation \( 4(3x - 2) = -24 \), follow these steps:

1. Distribute the 4 on the left side of the equation:

\[
12x - 8 = -24
\]

2. Next, add 8 to both sides to isolate the term with \( x \):

\[
12x - 8 + 8 = -24 + 8
\]
\[
12x = -16
\]

3. Now, divide both sides by 12 to solve for \( x \):

\[
x = \frac{-16}{12}
\]

4. Simplify the fraction:

\[
x = \frac{-4}{3}
\]

Thus, the value of \( x \) is \( \frac{-4}{3} \).

Answer 4

To solve the equation \(-2(4 + n) = 24\), we can follow these steps in the correct order:

1. **Distribute the -2**:
\[
-2 \cdot 4 - 2 \cdot n = 24
\]
This simplifies to:
\[
-8 - 2n = 24
\]

2. **Add 8 to both sides** to isolate the term with \(n\):
\[
-8 + 8 - 2n = 24 + 8
\]
This simplifies to:
\[
-2n = 32
\]

3. **Divide both sides by -2** to solve for \(n\):
\[
n = \frac{32}{-2}
\]
This simplifies to:
\[
n = -16
\]

Thus, the steps in order are:

1. Distribute \(-2\).
2. Add 8 to both sides.
3. Divide by -2 to solve for \(n\).

The final solution is \( n = -16 \).

Answer 5

To "distribute the -2" means to apply the multiplication of \(-2\) to each term inside the parentheses. This is a common algebraic technique used when you have an expression in the form \(a(b + c)\) or \(a(b - c)\), where \(a\) is a coefficient and \(b\) and \(c\) are terms.

In your equation \(-2(4 + n)\):

1. Apply \(-2\) to \(4\):
\[
-2 \cdot 4 = -8
\]

2. Apply \(-2\) to \(n\):
\[
-2 \cdot n = -2n
\]

So, when you combine those two results, \(-2(4 + n)\) becomes:
\[
-8 - 2n
\]

Therefore, distributing \(-2\) helps you remove the parentheses and rewrite the equation in a simpler form. The equation \(-2(4 + n) = 24\) transforms into:
\[
-8 - 2n = 24
\]