Solving the Equation 2(x + 1) = 6x – 46 and Understanding Math Terminology

2 (x + 1) = 6x – 46

To solve the equation 2(x + 1) = 6x – 46, we need to simplify and isolate the variable x

To solve the equation 2(x + 1) = 6x – 46, we need to simplify and isolate the variable x.

Step 1: Distribute the 2 on the left side of the equation.
2(x + 1) becomes 2x + 2.

So, the equation now becomes 2x + 2 = 6x – 46.

Step 2: Bring all the terms with x on one side and the constants on the other side.
Subtract 2x from both sides to get:
2x – 2x + 2 = 6x – 2x – 46
This simplifies to:
2 = 4x – 46.

Step 3: Isolate the variable x.
Add 46 to both sides of the equation to get:
2 + 46 = 4x – 46 + 46.
This simplifies to:
48 = 4x.

Step 4: Solve for x.
To isolate x, divide both sides of the equation by 4:
48/4 = (4x)/4.
This simplifies to:
12 = x.

So, the solution to the equation 2(x + 1) = 6x – 46 is x = 12.

Next, let’s look at some definitions:

1. Equation: An equation is a mathematical statement that contains an equal sign (=) and indicates that two expressions or values are equal. Equations are used to solve for unknown variables.

2. Variable: In mathematics, a variable is a symbol that represents a quantity that can change or vary. Variables are commonly denoted by letters such as x, y, or z.

3. Distributive Property: The distributive property is a fundamental property in algebra that allows you to multiply a single term by grouping it with each term inside parentheses. It states that for any real numbers a, b, and c: a(b + c) = ab + ac.

4. Simplify: When we simplify an expression or equation, we perform operations to reduce its complexity or make it easier to understand. This can involve combining like terms, applying mathematical rules, or eliminating unnecessary elements.

5. Isolate: To isolate a variable in an equation means to rewrite the equation in a way that the variable is alone on one side of the equation, with all other terms on the other side. This allows us to easily determine the value of the variable.

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