Problem 179 Solve the following equations wi... [FREE SOLUTION]

Chapter 2: Problem 179

Solve the following equations with constants on both sides. $$3 m+9=-15$$

Short Answer

Expert verified

m = -8

Step by step solution

Subtract 9 from both sides

To isolate the term with the variable (3m), subtract 9 from both sides of the equation: 3m + 9 - 9 = -15 - 9, which simplifies to 3m = -24.

Divide by 3

Next, divide both sides of the equation by 3 to solve for m : 3m / 3 = -24 / 3, which simplifies to m = -8.

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Key Concepts

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

Isolate Variable

To solve a linear equation, the primary goal is to isolate the variable. This means you need to get the variable (like $ m $) by itself on one side of the equation. You can achieve this by using basic algebraic operations like addition, subtraction, multiplication, or division. In the equation $3m + 9 = -15$, we start by isolating $ 3m $.
We do this by performing the same operation on both sides of the equation to maintain balance.

Constants on Both Sides

When dealing with linear equations, you often encounter constants, or fixed values, on both sides of the equation. To isolate the variable, you need to move these constants away from the variable's term. For example, in the equation $3m + 9 = -15$, there is a constant (9) on the left-hand side and another constant (-15) on the right-hand side.
First, we move the 9 by subtracting it from both sides, simplifying the equation to $ 3m = -24 $. This step removes the constant near the variable, making it easier to solve for $ m $.

Division in Equations

After isolating the term with the variable, the next step often involves division. This is because the variable might still have a coefficient (a number multiplied by it). In our example of $ 3m = -24 $, the variable $ m $ is multiplied by 3. To solve for $ m $, divide both sides of the equation by the coefficient.
Dividing by 3 simplifies the equation to $ m = -8 $. This final step leaves you with the variable isolated and solved.

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91影视

Solve the following equations with constants on both sides. $$3 m+9=-15$$

Short Answer

Step by step solution

Subtract 9 from both sides

Divide by 3

Key Concepts

Isolate Variable

Constants on Both Sides

Division in Equations

One App. One Place for Learning.

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