Simplifying 2(4x+7)-3(2x-4)
When dealing with algebraic expressions, it's essential to simplify them to make them easier to work with. In this article, we'll explore how to simplify the expression 2(4x+7)-3(2x-4).
Step 1: Expand the Brackets
To begin, we need to expand the brackets using the distributive property of multiplication over addition. This means that we multiply each term inside the brackets by the coefficient outside the brackets.
2(4x+7) = 2(4x) + 2(7) = 8x + 14
-3(2x-4) = -3(2x) + (-3)(-4) = -6x + 12
Now, we can rewrite the original expression as:
8x + 14 - 6x + 12
Step 2: Combine Like Terms
Next, we'll combine like terms, which are terms with the same variable (x) or constants.
Combine the x-terms: 8x - 6x = 2x
Combine the constants: 14 + 12 = 26
So, the simplified expression is:
2x + 26
Conclusion
By following the steps outlined above, we've successfully simplified the expression 2(4x+7)-3(2x-4) to 2x + 26. This process involved expanding the brackets and combining like terms, resulting in a simplified expression that's easier to work with in algebraic manipulations.
