Simplify: $ 3x + 3 = 45 $. - Abu Waleed Tea
Simplify: How to Solve $ 3x + 3 = 45 $ Step by Step
Simplify: How to Solve $ 3x + 3 = 45 $ Step by Step
Solving a simple equation like $ 3x + 3 = 45 $ might seem straightforward, but mastering the process helps build strong algebraic foundations. In this article, we’ll break down step-by-step how to solve the equation $ 3x + 3 = 45 $, explain the logic behind each step, and offer practical tips to simplify the learning process — whether you're a student, teacher, or self-learner.
Understanding the Context
What is the Equation $ 3x + 3 = 45 $?
The expression $ 3x + 3 = 45 $ means that when you multiply an unknown number $ x $ by 3, then add 3, the result is 45. Our goal is to find the value of $ x $ that makes this equation true.
Step 1: Isolate the Term with $ x $
Key Insights
Start by subtracting 3 from both sides of the equation to eliminate the constant on the left side. This keeps the equation balanced.
$$
3x + 3 - 3 = 45 - 3
$$
$$
3x = 42
$$
Tip: Always perform the same operation on both sides to maintain equality.
Step 2: Solve for $ x $
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📰 Une entreprise produit des widgets qui circulent sur un marché avec une courbe de demande donnée par \( D(p) = 100 - 2p \), où \( p \) est le prix par widget. Le coût de production pour \( x \) widgets est donné par \( C(x) = 50x + 200 \). Si l'entreprise souhaite maximiser son profit, quel prix \( p \) devrait-elle facturer par widget ? 📰 D'abord, exprimez \( x \) en fonction de \( p \) : \( x = 100 - 2p \). 📰 La fonction de revenu \( R(p) \) est \( R(p) = p imes x = p(100 - 2p) = 100p - 2p^2 \).Final Thoughts
Now divide both sides by 3 to isolate $ x $:
$$
rac{3x}{3} = rac{42}{3}
$$
$$
x = 14
$$
Final Answer
$$
x = 14
$$
Check your work: Substitute $ x = 14 $ back into the original equation:
$ 3(14) + 3 = 42 + 3 = 45 $ — correct!
Why Simplifying Equations Matters
Understanding how to simplify expressions and solve equations is essential for academic success in math and related STEM fields. Learning to simplify $ 3x + 3 = 45 $ builds problem-solving skills applicable to complex problems in algebra, calculus, and beyond.
