Problem 67 Solve the equation. $$-5+7=5 x... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 67

Solve the equation. $$-5+7=5 x-4(x-1)$$

Short Answer

Expert verified

-2

Step by step solution

- Simplify the Equation

Start by simplifying the right side of the equation. Distribute the frames the variable

- Combine Like Terms

Once you've simplified the right-hand side, combine any like terms on both sides of the equation.

- Isolate the Variable

Move all terms involving the variable to one side of the equation and constant terms to the other side.

- Solve for the Variable

Simplify the equation to find the value of the variable.

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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 crucial step in solving linear equations. It allows you to simplify complex expressions by distributing multiplication over addition or subtraction. For example, in the equation $ 5 x-4(x-1) $, you need to distribute $ -4 $ to both $ x $ and $ -1 $, which gives: \[ -4 \times x = -4x \] and \[ -4 \times (-1) = 4 \]. Now the equation looks like this: \[ -5 + 7 = 5x - 4x + 4 \]. Distributing can help in breaking down the problem into easier steps.

Combining Like Terms

After using the distributive property, the next step is combining like terms. Like terms are terms that have the same variables raised to the same power. In our example, $ 5x $ and $ -4x $ are like terms. Combining them involves adding or subtracting their coefficients: \[ 5x - 4x = x \]. After combining, the equation simplifies to: \[ -5 + 7 = x + 4 \]. This process helps simplify the equation further, making it easier to solve.

Isolating Variables

Isolating the variable means rearranging the equation to get the variable alone on one side. This helps you find the value of the variable. In our simplified equation, \[ -5 + 7 = x + 4 \], first, combine constants on the left side: \[ 2 = x + 4 \]. Next, subtract 4 from both sides to isolate $ x $: \[ 2 - 4 = x \]. This further simplifies to: \[ -2 = x \].

Simplifying Equations

Simplifying equations is the final step in solving for the variable. It involves performing basic arithmetic operations to isolate the variable completely. In the example: \[ 2 - 4 = x \], simplify further to get \[ -2 = x \]. Now, $ x $ has been isolated, and you have the solution $ x = -2 $. Simplifying equations ensures that the problem is solved in the most straightforward way possible. Always check your final answer by plugging it back into the original equation to verify it is correct.

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91影视

Solve the equation. $$-5+7=5 x-4(x-1)$$

Short Answer

Step by step solution

- Simplify the Equation

- Combine Like Terms

- Isolate the Variable

- Solve for the Variable

Key Concepts

Distributive Property

Combining Like Terms

Isolating Variables

Simplifying Equations

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