Solving the Simple Linear Equation: How 3x + 5x = 40 Leads to x = 5

Learning basic algebra helps build stronger problem-solving skills, even in simple equations. One of the most straightforward examples is solving the equation 3x + 5x = 40, which quickly reveals the value of x—and shows how powerful basic math can be.

Breaking Down the Equation

Understanding the Context

Start with the equation:
3x + 5x = 40

Notice that both terms on the left involve x. We can combine like terms:
3x + 5x combines to 8x, giving us:
8x = 40

This step simplifies the problem by grouping similar elements, making it easier to isolate x.

Solving for x

[ANSWERED] 5 x 3x 40 0 7 x 49 14x 6 x 150 8 3x x 1 0 - Kunduz

Image Gallery

[ANSWERED] 5 x 3x 40 0 7 x 49 14x 6 x 150 8 3x x 1 0 - Kunduz
Solved: (x+3)(x+2)= (x-8)(x-3)= (x+5)(x-4)= (x-9)(x+3)= (x+5)(x-2)= (x ...
5) x² + 6x² + 5x-0 7) x² - 8x + 5 = 0 9) x + 13x² + | Chegg.com
Multiplication 8x5
Solved 3x-8 (x-3)(x-2) 2x-5 (x-3)(x-1) 15 х-3 х-2 16 x-3 х-1 | Chegg.com

Key Insights

Now, to find x, divide both sides of the equation by 8:
x = 40 ÷ 8
x = 5

This straightforward division confirms that when we add 3x and 5x, the total equals 40 only if x = 5.

Why This Equation Matters

At first glance, 3x + 5x = 40 might seem simple, but it illustrates key algebraic principles: combining like terms, solving for a variable, and checking results. These skills form the building blocks for more complex math, including equations used in science, engineering, and finance.

Final Check

Continue Reading

Question: Find the least common multiple of 18, 24, and 40.
Question: How many positive 5-digit numbers are divisible by 15 and have a digit sum equal to 15?
Solution: A number divisible by 15 must be divisible by both 3 and 5. For divisibility by 5, it must end in 0 or 5. For divisibility by 3, the digit sum must be divisible by 3. Since the digit sum is 15, which is divisible by 3, any number with digit sum 15 automatically satisfies divisibility by 3. So we only need to count 5-digit numbers with digit sum 15 and last digit 0 or 5.

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Final Thoughts

To verify, substitute x = 5 back into the original equation:
3(5) + 5(5) = 15 + 25 = 40, which is correct.

Conclusion

Solving 3x + 5x = 40 and finding x = 5 demonstrates how clear, step-by-step reasoning transforms a basic equation into a confident conclusion. Whether you're a student or brushing up on fundamentals, mastering such equations strengthens logical thinking and sets the stage for tackling advanced math challenges.

Keywords: 3x + 5x = 40, solving linear equations, algebraic basics, how to solve x, step-by-step math, math problem solving, x equals 5, simple equation solution.