Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x-5 = 7

Verified step by step guidance

1. Start with the given equation: \$2x - 5 = 7$.
2. Add 5 to both sides of the equation to isolate the term with \(x\): \$2x - 5 + 5 = 7 + 5\(, which simplifies to \)2x = 12$.
3. Divide both sides of the equation by 2 to solve for \(x\): \(\frac{2x}{2} = \frac{12}{2}\), which simplifies to \(x = 6\).
4. Interpret the solution: since \(x = 6\) satisfies the original equation, this is a conditional equation with one solution.
5. Conclude that the equation is conditional because it is true for a specific value of \(x\) (namely \(x = 6\)), not for all values (identity) or no values (inconsistent).

Key Concepts

Solving Linear Equations

Solving linear equations involves isolating the variable on one side of the equation using inverse operations such as addition, subtraction, multiplication, or division. For example, in 2x - 5 = 7, you add 5 to both sides and then divide by 2 to find x.

Types of Equations: Identity, Conditional, and Inconsistent

An identity is true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solution. After solving, you determine which type applies based on the solution set.

Checking Solutions

After finding a solution, substitute it back into the original equation to verify its validity. This step confirms whether the solution satisfies the equation, helping to classify the equation correctly.