Problem 34 Solve each equation, and check y... [FREE SOLUTION]

Chapter 2: Problem 34

Solve each equation, and check your solution. $$ 9 x+1=8 x+4 $$

Short Answer

Expert verified

The solution is $x = 3$. This satisfies the original equation.

Step by step solution

- Move Variables to One Side

Subtract $8x$ from both sides of the equation to move all the variable terms to one side.\[9x + 1 - 8x = 8x + 4 - 8x\]Simplifying this gives:\[x + 1 = 4\]

- Isolate the Variable

Subtract 1 from both sides to isolate $x$:\[x + 1 - 1 = 4 - 1\]Simplifying this gives:\[x = 3\]

- Check the Solution

Substitute $x = 3$ back into the original equation to verify the solution:\[9(3) + 1 = 8(3) + 4\]Calculate both sides to check:\[27 + 1 = 24 + 4\]\[28 = 28\]Since both sides are equal, the solution is correct.

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Key Concepts

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

Variable Isolation

When solving linear equations, isolating the variable is crucial. This means getting the variable on one side of the equation and everything else on the other. In our problem, we started with the equation $9x + 1 = 8x + 4$. By subtracting $8x$ from both sides, we grouped all the $x$-terms together. This step gave us the simplified equation $x + 1 = 4$ . Next, to isolate $x$, we subtracted 1 from both sides, leading to $x = 3$. This means $x$ is now alone and equals 3. Isolating the variable helps make the equation cleaner and easier to solve.

Equation Verification

Verifying the solution is an essential step in solving any equation. To check our solution for the equation $9x + 1 = 8x + 4$, we substitute $x = 3$ back into the original equation. Let's break it down: $9(3) + 1 = 8(3) + 4$ becomes $27 + 1 = 24 + 4$, which simplifies to $28 = 28$. Both sides are equal, meaning our solution is correct. Verification helps you ensure that no mistakes were made during the isolation process.

Simplifying Equations

Simplifying equations makes them easier to work with. Start by combining like terms. In our initial equation $9x + 1 = 8x + 4$, we combined the $x$-terms by subtracting $8x$ from both sides, which resulted in $x + 1 = 4$. This simplification paves the way for easier solving. Further simplifying involved moving the constant term (1) to the other side by subtraction, leading us to $x = 3$. These small steps make the larger equation manageable, solving the equation piece by piece.

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91影视

Solve each equation, and check your solution. $$ 9 x+1=8 x+4 $$

Short Answer

Step by step solution

- Move Variables to One Side

- Isolate the Variable

- Check the Solution

Key Concepts

Variable Isolation

Equation Verification

Simplifying Equations

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