What is the solution of the equation (-8x + 6) + 8 = -7(x + 4)?
Understand the Problem
The question is asking for the solution to the equation by manipulating both sides and solving for x. We can distribute the -7 on the right side and then combine like terms to find the value of x.
Answer
$x = \frac{5}{3}$
Answer for screen readers
The final solution for $x$ is:
$$ x = \frac{5}{3} $$
Steps to Solve
- Distribute the -7 on the right side
We start by distributing the -7 to both terms inside the parentheses on the right side of the equation. If our equation is $ x + 3 = -7(2x - 4) $, it becomes:
$$ x + 3 = -14x + 28 $$
- Combine like terms
Next, we want to isolate $x$. We'll move $-14x$ to the left side by adding $14x$ to both sides:
$$ x + 14x + 3 = 28 $$
This simplifies to:
$$ 15x + 3 = 28 $$
- Subtract 3 from both sides
To isolate the term with $x$, we need to get rid of the constant 3 on the left side. We do this by subtracting 3 from both sides:
$$ 15x + 3 - 3 = 28 - 3 $$
This simplifies to:
$$ 15x = 25 $$
- Divide by 15 to solve for x
Finally, we solve for $x$ by dividing both sides by 15:
$$ x = \frac{25}{15} $$
This reduces to:
$$ x = \frac{5}{3} $$
The final solution for $x$ is:
$$ x = \frac{5}{3} $$
More Information
The solution $\frac{5}{3}$ can also be expressed as approximately 1.67, but it's typically left as a fraction for exactness. This shows that $x$ is slightly greater than 1.5.
Tips
- Forgetting to distribute the negative sign correctly can lead to incorrect terms.
- Miscalculating when combining like terms, leading to an incorrect equation.
- Not simplifying the fraction to its lowest terms if applicable.
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