Solve the Equation: x + (x + 1) + (x + 2) = 33 – Step-by-Step Explanation

Understanding and solving simple algebraic equations is a foundational math skill with real-world applications. Whether you’re measuring quantities, planning budgets, or analyzing data, being able to translate word problems into math equations ensures accuracy. In this article, we’ll explore how to solve the equation x + (x + 1) + (x + 2) = 33, simplify it step-by-step, and verify the solution. We’ll also explain why this basic algebra is crucial in everyday problem-solving.

The Original Equation:

x + (x + 1) + (x + 2) = 33

Understanding the Context

This equation models a scenario where three consecutive integers—x, x+1, and x+2—are added together, and the total equals 33. Recognizing that these represent sequential numbers helps speed up simplification.

Step 1: Combine Like Terms

Start by removing the parentheses and combining all x-terms:
x + (x + 1) + (x + 2) = x + x + 1 + x + 2

Combine the x-values:
x + x + x = 3x
1 + 2 = 3

So the left side simplifies to:
3x + 3

x + (x+1) + (x+2) = 3x + 3 = 33

Key Insights

Now the equation becomes:
3x + 3 = 33

Step 2: Isolate the Variable

Subtract 3 from both sides to isolate the term with x:
3x + 3 – 3 = 33 – 3
3x = 30

Step 3: Solve for x

Divide both sides by 3:
3x ÷ 3 = 30 ÷ 3
x = 10

Step 4: Verify the Solution

Check by plugging x = 10 back into the original equation:
x + (x + 1) + (x + 2) = 10 + (10 + 1) + (10 + 2)
= 10 + 11 + 12 = 33

This confirms the solution is correct.

Continue Reading

The altitude corresponding to a side is $ h = \frac{2A}{\text{side}} $. The longest altitude corresponds to the shortest side, which is 13 cm:
h_{\text{longest}} = \frac{2 \cdot 84}{13} = \frac{168}{13} \approx 12.92
Thus, the length of the longest altitude is $ \boxed{\frac{168}{13}} $ cm.

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Final Thoughts

Why Solving Linear Equations Like This Matters

Linear equations such as x + (x + 1) + (x + 2) = 33 appear in budgeting—calculating predicted monthly expenses—science in measuring successive data points, and in crafting equations for engineering and computer science. Mastering step-by-step algebra helps build logical thinking and precision in real-life decision-making.

Conclusion

The solution to x + (x + 1) + (x + 2) = 33 is x = 10. By combining like terms and isolating the variable, we efficiently solve simple linear equations that reflect everyday situations. Practice these steps to strengthen your math foundation and tackle more complex problems with confidence.

Keywords: algebra, solve x + (x + 1) + (x + 2) = 33, linear equations, step-by-step math, solve x, math problem-solving, basic algebra, educational math, math skills development

Meta Description: Learn how to solve the equation x + (x + 1) + (x + 2) = 33 step-by-step, verify your answers, and understand why this foundational algebra skill matters in everyday problem-solving.