Problem 41 Solve the equation. $$2(1-m)=5... [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 41

Solve the equation. $$2(1-m)=5-3 m$$

Short Answer

Expert verified

m = 3

Step by step solution

- Distribute the multiplication

Distribute the 2 across the terms inside the parentheses on the left-hand side of the equation. This means you should calculate 2*1 and 2*(-m). The equation becomes: 2 - 2m = 5 - 3m

- Add 3m to both sides

To eliminate the variable on the right-hand side, add 3m to both sides of the equation. This will give: 2 - 2m + 3m = 5 - 3m + 3m Simplify the equation to: 2 + m = 5

- Subtract 2 from both sides

To isolate the variable, subtract 2 from both sides of the equation. This will give: 2 + m - 2 = 5 - 2 Simplify the equation to: m = 3

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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 key concept in algebra that helps simplify expressions. It allows you to multiply a single term by each term inside parentheses. In our exercise, we apply the distributive property to the equation 2(1-m). This means you multiply 2 by 1 and then by -m.
Here's the step-by-step process:

First, multiply 2 by 1, giving you 2.
Next, multiply 2 by -m, resulting in -2m.

After distributing, the original equation 2(1-m) transforms into 2 - 2m. Now, the equation becomes 2 - 2m = 5 - 3m. Applying the distributive property correctly is crucial for simplifying and solving linear equations.

Isolation of Variable

Isolating the variable is an essential step in solving equations. The goal is to get the variable (m) by itself on one side of the equation. To do this, follow these steps:
Add or subtract terms to both sides of the equation to move all variable terms to one side and all constant terms to the other.
In the exercise, our goal is to move the -3m to the left side. We do this by adding 3m to both sides:

The equation: 2 - 2m = 5 - 3m
Add 3m to both sides: 2 - 2m + 3m = 5 - 3m + 3m
Simplify to get: 2 + m = 5

Now the variable m is on the left side, getting closer to being isolated.

Simplification Steps

Simplifying equations is the final step to solving for the variable. These steps make the equation easier to work with and help find the solution. The simplification involves combining like terms and performing basic arithmetic operations.

In the exercise, after adding 3m to both sides, we have 2 + m = 5.
To isolate m, subtract 2 from both sides: 2 + m - 2 = 5 - 2
Simplifying, you get m = 3.

Now the equation is simplified, and we have found the value of m. Simplification steps are critical as they help in reducing the equation to its simplest form, making the problem easier to solve.

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91影视

Solve the equation. $$2(1-m)=5-3 m$$

Short Answer

Step by step solution

- Distribute the multiplication

- Add 3m to both sides

- Subtract 2 from both sides

Key Concepts

Distributive Property

Isolation of Variable

Simplification Steps

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