When faced with an algebraic expression such as 2(8x) + 4(2x) – 5, it may seem daunting at first. However, with a systematic approach and understanding of algebraic principles, you can find the solution to this equation. In this article, we will break down each step to reach the final answer.
Step 1: Distribute the coefficients
First, we need to distribute the coefficients in the expression. This means multiplying the numbers outside the parentheses with the terms inside the parentheses.
- 2(8x) = 16x
- 4(2x) = 8x
Step 2: Combine like terms
Next, we combine like terms in the expression by adding or subtracting coefficients of the same variable.
- 16x + 8x = 24x
Step 3: Subtract 5
Finally, we subtract 5 from the combined like terms.
- 24x – 5
The final solution to 2(8x) + 4(2x) – 5 is 24x – 5.
By following these steps, we were able to simplify the given expression and find the solution. Understanding the basic principles of algebra, such as distributing coefficients and combining like terms, is essential in solving equations like this one.
Practice problems:
Here are a few practice problems for you to try on your own:
- Solve for x: 3(4x) + 2(x) – 7
- Solve for y: 5(2y) – 3(5y) + 10
Remember to follow the steps we discussed earlier to simplify the expressions and find the solutions. Practice makes perfect!
Conclusion
Algebraic expressions may seem complex at first, but with a structured approach and knowledge of fundamental algebraic principles, you can simplify and solve them. In the case of 2(8x) + 4(2x) – 5, we applied steps such as distributing coefficients, combining like terms, and subtracting constants to reach the final solution of 24x – 5.
Remember to practice solving similar equations to strengthen your algebraic skills. With patience and persistence, you can conquer any algebraic expression that comes your way!
