Step-by-Step Solution | Solving the Equation x + 3 = 3(11 – 3x) and Important Terms Explained

x + 3 = 3 (11 – 3x)

To solve the equation x + 3 = 3(11 – 3x), we will follow these steps:

Step 1: Distribute the 3 on the right side of the equation:
x + 3 = 33 – 9x

Step 2: Combine like terms:
10x + 3 = 33

Step 3: Subtract 3 from both sides to isolate the x term:
10x = 30

Step 4: Divide both sides by 10 to solve for x:
x = 3

So, the solution to the equation x + 3 = 3(11 – 3x) is x = 3

To solve the equation x + 3 = 3(11 – 3x), we will follow these steps:

Step 1: Distribute the 3 on the right side of the equation:
x + 3 = 33 – 9x

Step 2: Combine like terms:
10x + 3 = 33

Step 3: Subtract 3 from both sides to isolate the x term:
10x = 30

Step 4: Divide both sides by 10 to solve for x:
x = 3

So, the solution to the equation x + 3 = 3(11 – 3x) is x = 3.

Now, let’s define a few important terms related to equations:

1. Equation: An equation is a mathematical statement that says two expressions are equal. It consists of an equal sign (=) and expressions on both sides of the equal sign.

2. Variable: A variable is a symbol that represents an unknown value in an equation or expression. In the equation mentioned earlier, x is the variable.

3. Coefficient: In an equation, the coefficient is the numerical factor multiplied by the variable. For example, in the equation 5x + 2 = 17, the coefficient of x is 5.

4. Distributive Property: The distributive property is a rule in mathematics that allows you to multiply a number by a sum or difference of two or more terms. For example, in the equation 3(x + 2), you can distribute the 3 to both terms inside the parentheses: 3(x) + 3(2) = 3x + 6.

5. Solution: In the context of an equation, a solution is a value that makes the equation true when substituted into the variable. For example, in the equation 2x – 5 = 7, the solution is x = 6, since when you substitute 6 for x, the equation becomes 2(6) – 5 = 7, which is true.

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