Problem 208 Solve the following equations wi... [FREE SOLUTION]

Chapter 2: Problem 208

Solve the following equations with variables and constants on both sides. $$7 s+12=5+4 s$$

Short Answer

Expert verified

The solution is $s = \frac{-7}{3}$.

Step by step solution

Move Variable Terms

Move all terms containing the variable to one side of the equation. Subtract $4s$ from both sides:\[7s + 12 - 4s = 5 + 4s - 4s\]This simplifies to:\[3s + 12 = 5\]

Move Constant Terms

Move all constant terms to the opposite side by subtracting 12 from both sides:\[3s + 12 - 12 = 5 - 12\]This simplifies to:\[3s = -7\]

Solve for the Variable

Isolate the variable by dividing both sides by 3:\[s = \frac{-7}{3}\]

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Key Concepts

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

variables on both sides

When solving linear equations, you often encounter variables on both sides. This means you have the variable term (like $4s or 7s)$ on both sides of the equals sign. The goal is to move all the variables to one side to combine them and simplify the equation.

So, if you start with an equation like: 7s + 12 = 5 + 4s

The first step is to get all variable terms on one side. Usually, you achieve this by subtracting the smaller variable term from both sides. For example, subtracting $4s$ from both sides gives you:

7s + 12 - 4s = 5 + 4s - 4s

This simplifies to:

3s + 12 = 5

Now, you have simplified to an equation with all variables on one side.

simplifying equations

After moving the variables to one side, the next step is simplifying the equation. Simplifying means making the equation easier to solve by performing basic arithmetic operations.

In our example:

3s + 12 = 5

You need to isolate the terms involving the variable $s$ from the constants (numbers without variables). This means moving the constant term on the same side as the variable $s$ to the opposite side. You can achieve this by subtracting 12 from both sides:

3s + 12 - 12 = 5 - 12

This action simplifies the equation to:

3s = -7

Remember, always perform the same arithmetic operation (addition, subtraction, multiplication, division) on both sides of the equation to maintain balance.

isolating variables

Finally, you need to isolate the variable. This means getting the variable all by itself on one side of the equation so that you have $s=$ some number. In our simplified equation:

3s = -7

The variable $s$ is already alone except for being multiplied by 3. To isolate $s$, you need to divide both sides by 3:

s = \frac{-7}{3}

This action gives you the solution to the equation, $s = \frac{-7}{3}$. Now, the variable $s$ is isolated and we have found its value.

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91影视

Solve the following equations with variables and constants on both sides. $$7 s+12=5+4 s$$

Short Answer

Step by step solution

Move Variable Terms

Move Constant Terms

Solve for the Variable

Key Concepts

variables on both sides

simplifying equations

isolating variables

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