Ch. 1 - Equations and Inequalities

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 6

Chapter 2, Problem 6

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

Verified step by step guidance

Start by writing down the given equation: \(2x + 5 = x - 3\).

To isolate the variable \(x\), subtract \(x\) from both sides: \(2x + 5 - x = x - 3 - x\), which simplifies to \(x + 5 = -3\).

Next, subtract 5 from both sides to get \(x\) alone: \(x + 5 - 5 = -3 - 5\), which simplifies to \(x = -8\).

The solution set is the value(s) of \(x\) that satisfy the equation. Here, the solution set is {\(-8\)}.

Since the solution set given in the problem is also {\(-8\)}, the statement is true.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solving Linear Equations

Solving linear equations involves isolating the variable on one side to find its value. This typically requires using inverse operations such as addition, subtraction, multiplication, or division to simplify the equation step-by-step.

Checking Solutions

After finding a solution, substituting it back into the original equation verifies its correctness. If both sides of the equation are equal after substitution, the solution is valid; otherwise, it is not.

Solution Set

The solution set is the collection of all values that satisfy the equation. For linear equations, the solution set usually contains a single value or is empty if no solution exists.

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