4(3x - 2) = -24
determine the value of x
5 answers
To solve the equation \( 4(3x - 2) = -24 \), follow these steps:
Distribute the 4 on the left side of the equation:
\[ 12x - 8 = -24 \]
Next, add 8 to both sides to isolate the term with \( x \):
\[ 12x - 8 + 8 = -24 + 8 \] \[ 12x = -16 \]
Now, divide both sides by 12 to solve for \( x \):
\[ x = \frac{-16}{12} \]
Simplify the fraction:
\[ x = \frac{-4}{3} \]
Thus, the value of \( x \) is \( \frac{-4}{3} \).
To solve the equation \(-2(4 + n) = 24\), we can follow these steps in the correct order:
Distribute the -2: \[ -2 \cdot 4 - 2 \cdot n = 24 \] This simplifies to: \[ -8 - 2n = 24 \]
Add 8 to both sides to isolate the term with \(n\): \[ -8 + 8 - 2n = 24 + 8 \] This simplifies to: \[ -2n = 32 \]
Divide both sides by -2 to solve for \(n\): \[ n = \frac{32}{-2} \] This simplifies to: \[ n = -16 \]
Thus, the steps in order are:
The final solution is \( n = -16 \).
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 \(-2(4 + n)\):
Apply \(-2\) to \(4\): \[ -2 \cdot 4 = -8 \]
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: \[ -8 - 2n = 24 \]
