Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 3-5(2x + 1) - 2(x-4) = 0

Verified step by step guidance

1. Start by distributing the constants outside the parentheses to each term inside the parentheses. For the expression \$3 - 5(2x + 1) - 2(x - 4) = 0\(, distribute \)-5\( to both \)2x\( and \)1\(, and distribute \)-2\( to both \)x\( and \)-4$.
2. Rewrite the equation after distribution: \$3 - 10x - 5 - 2x + 8 = 0$.
3. Combine like terms on the left side of the equation. Group the constant terms together and the \(x\) terms together.
4. Simplify the equation to the form \(ax + b = 0\), where \(a\) and \(b\) are constants.
5. Solve for \(x\) by isolating the variable: subtract or add constants to both sides and then divide both sides by the coefficient of \(x\). After finding the solution, determine if the equation is an identity (true for all \(x\)), conditional (true for specific \(x\)), or inconsistent (no solution).

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, and division. The goal is to find the value of the variable that makes the equation true.

Distributive Property

The distributive property allows you to multiply a single term by each term inside parentheses, expressed as a(b + c) = ab + ac. This property is essential for simplifying expressions before solving equations.

Types of Equations: Identity, Conditional, and Inconsistent

An identity is true for all variable values, a conditional equation is true for specific values, and an inconsistent equation has no solution. Classifying the equation after solving helps understand the nature of its solutions.