3x = 2 (7 + 5x)
To solve the equation 3x = 2(7 + 5x), we can start by simplifying both sides of the equal sign
To solve the equation 3x = 2(7 + 5x), we can start by simplifying both sides of the equal sign.
On the right side of the equation, we distribute the 2 to both 7 and 5x:
3x = 14 + 10x
Next, let’s move all the terms involving x to one side of the equation. We can start by subtracting 10x from both sides:
3x – 10x = 14 + 10x – 10x
This simplifies to:
-7x = 14
Now, we can solve for x by dividing both sides of the equation by -7:
-7x / -7 = 14 / -7
This gives us:
x = -2
So, the solution to the equation 3x = 2(7 + 5x) is x = -2.
Definitions:
1. Equation: An equation is a mathematical statement that shows the equality of two expressions. It typically consists of variables, constants, and mathematical operations.
2. Term: In mathematics, a term refers to a single expression that is part of a larger algebraic expression or equation. Each term can have variables and coefficients.
3. Distributive Property: The distributive property is a property of numbers that states that multiplying a number by a sum or difference is the same as multiplying the number by each addend individually and then adding or subtracting the results. In algebra, this property is often used to simplify expressions by expanding them.
4. Simplifying: In mathematics, simplifying refers to the process of rewriting an expression in a simpler or more reduced form. This typically involves combining like terms, removing parentheses, and applying mathematical operations to simplify calculations.
5. Solution: In mathematics, a solution refers to the value or values that satisfy a given equation or inequality. For equations, a solution is the value(s) of the variable that make the equation true.
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