Decide whether each statement is true or false. The solution set of 2x+5=x -3 is {-8}.

Verified step by step guidance

1. Step 1: Start by solving the equation \(2x + 5 = x - 3\).
2. Step 2: Subtract \(x\) from both sides to isolate terms with \(x\) on one side: \(2x - x + 5 = -3\).
3. Step 3: Simplify the equation: \(x + 5 = -3\).
4. Step 4: Subtract 5 from both sides to solve for \(x\): \(x = -3 - 5\).
5. Step 5: Simplify the right side to find \(x\). Compare this value to the proposed solution set \{-8\} to determine if the statement is true or false.

Key Concepts

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. This typically requires isolating the variable on one side of the equation through algebraic operations such as addition, subtraction, multiplication, and division. Understanding how to manipulate equations is essential for determining the solution set.

Solution Set

The solution set of an equation is the collection of all values that satisfy the equation. For linear equations, this often consists of a single value, a range of values, or no values at all. Identifying the correct solution set is crucial for verifying the truth of statements regarding the equation.

Verification of Solutions

Verification of solutions involves substituting the proposed solution back into the original equation to check if it holds true. This step is vital to confirm whether the solution set provided is accurate. In this case, substituting -8 into the equation will determine if it is indeed a valid solution.