Problem 57 Solve equation. \(-2(x-2)+5 x=... [FREE SOLUTION]

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Chapter 8: Problem 57

Solve equation. \(-2(x-2)+5 x=10\)

Short Answer

Expert verified

x = 2

Step by step solution

- Distribute / -2

Distribute / -2 through the parentheses. \(-2(x-2) = -2x + 4\), so our equation transforms to: \(-2x + 4 + 5x = 10\)

- Combine Like Terms

Combine the like terms on the left side of the equation. \(-2x + 5x + 4 = 10\) simplifies to \(3x + 4 = 10\)

- Isolate the Variable

Subtract 4 from both sides to isolate terms with x: \(3x + 4 - 4 = 10 - 4\), which reduces to \(3x = 6\)

- Solve for x

Divide both sides by 3 to solve for x: \(x = \frac{6}{3}\), which simplifies to \(x = 2\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property

The distributive property is a significant concept in algebra. It lets you multiply a single term by terms within parentheses. Imagine you have \(a(b + c)\). Using the distributive property, you can simplify it to \(ab + ac\). For our exercise, we applied the distributive property to \(-2(x-2)\). This means we multiply \(-2\) by each term inside the parentheses.

So, \(-2(x-2) = -2 \times x + (-2 \times -2) = -2x + 4\).
This transformation helps make the equation easier to solve.

Combining Like Terms

Combining like terms is an essential algebraic operation that simplifies equations. Like terms are terms that have the same variable raised to the same power. For instance, \(3x\) and \(5x\) are like terms because both have the variable \(x\).

In our exercise, we had \(-2x + 4 + 5x\). The like terms here are \(-2x\) and \(5x\). Combining them gives us \( -2x + 5x = 3x\). After this step, our equation is now \(3x + 4 = 10\), making it simpler to solve.

Isolating the Variable

Isolating the variable means getting the variable (like \(x\)) on its own on one side of the equation. It helps us find the value of the variable.

Start with the equation: \(3x + 4 = 10\). We need to eliminate the 4 on the left side.

We do this by subtracting 4 from both sides, resulting in: \(3x + 4 - 4 = 10 - 4\). This simplifies to \(3x = 6\). Now, \(x\) is closer to being isolated.

Algebraic Operations

Algebraic operations are the basic operations used in algebra: addition, subtraction, multiplication, and division.

In our exercise, we followed these operations step-by-step to solve for \(x\).

Finally, to isolate \(x\), we divide both sides by 3: \(3x/3 = 6/3\), which simplifies to \(x = 2\).

Following these steps methodically makes solving linear equations simple and clear.

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91影视

Solve equation. \(-2(x-2)+5 x=10\)

Short Answer

Step by step solution

- Distribute / -2

- Combine Like Terms

- Isolate the Variable

- Solve for x

Key Concepts

Distributive Property

Combining Like Terms

Isolating the Variable

Algebraic Operations

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