Solve and check each linear equation. 3(x - 1) = 21

Verified step by step guidance

1. Distribute the 3 on the left-hand side of the equation to eliminate the parentheses. This means multiplying 3 by each term inside the parentheses: $3(x\; -\; 1)\; =\; 3x\; -\; 3$. The equation becomes $3x\; -\; 3\; =\; 21$.
2. Add 3 to both sides of the equation to isolate the term with the variable on one side. This gives: $3x\; -\; 3\; +\; 3\; =\; 21\; +\; 3$, simplifying to $3x\; =\; 24$.
3. Divide both sides of the equation by 3 to solve for $x$. This gives: $x\; =\; \backslash (\backslash frac\{24\}\{3\}\backslash )$.
4. Simplify the fraction $\backslash (\backslash frac\{24\}\{3\}\backslash )$ to find the value of $x$. This step completes the solution for $x$.
5. Check your solution by substituting the value of $x$ back into the original equation $3(x\; -\; 1)\; =\; 21$. Verify that both sides of the equation are equal.

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed. It typically takes the form ax + b = c, where a, b, and c are constants, and x is the variable. Solving a linear equation involves isolating the variable to find its value, which satisfies the equation.

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property is essential for simplifying expressions where a term is multiplied by a sum or difference. In the context of the given equation, applying the distributive property allows us to eliminate parentheses and simplify the equation for easier solving.

Checking Solutions

Checking solutions involves substituting the found value of the variable back into the original equation to verify its correctness. This step ensures that the solution satisfies the equation, confirming that no errors were made during the solving process. It is a crucial part of solving linear equations to ensure accuracy.