What is the solution to -2.5(4x - 4) = -6?
Understand the Problem
The question is asking to solve the equation -2.5(4x - 4) = -6, which involves finding the value of x that satisfies this equation.
Answer
The solution is $x = \frac{8}{5}$.
Answer for screen readers
The solution to the equation is
$$ x = \frac{8}{5} $$
Steps to Solve
- Distribute the -2.5
Distribute -2.5 across the terms inside the parentheses:
$$ -2.5(4x) - (-2.5)(4) = -6 $$
This simplifies to:
$$ -10x + 10 = -6 $$
- Isolate the variable term
Next, we want to isolate the term with the variable $x$. Subtract 10 from both sides:
$$ -10x + 10 - 10 = -6 - 10 $$
This simplifies to:
$$ -10x = -16 $$
- Solve for x
To solve for $x$, divide both sides by -10:
$$ x = \frac{-16}{-10} $$
This reduces to:
$$ x = \frac{16}{10} = \frac{8}{5} $$
The solution to the equation is
$$ x = \frac{8}{5} $$
More Information
The result $\frac{8}{5}$ can be converted to a decimal, which is 1.6. This means that if you substitute $x = 1.6$ back into the original equation, both sides will be equal.
Tips
- Forgetting to distribute the factor correctly. Ensure that each term inside the parentheses is multiplied by the factor outside.
- Not isolating the variable properly. It's important to follow the correct order of operations when rearranging the equation.
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