Solve and check each linear equation. 11x - (6x - 5) = 40

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Distribute the negative sign across the parentheses in the equation. This means rewriting \( 11x - (6x - 5) \) as \( 11x - 6x + 5 \). The equation becomes \( 11x - 6x + 5 = 40 \).

Combine like terms on the left-hand side of the equation. Combine \( 11x \) and \( -6x \) to get \( 5x \). The equation simplifies to \( 5x + 5 = 40 \).

Isolate the variable term \( 5x \) by subtracting 5 from both sides of the equation. This gives \( 5x = 35 \).

Solve for \( x \) by dividing both sides of the equation by 5. This gives \( x = \frac{35}{5} \).

Check your solution by substituting \( x \) back into the original equation \( 11x - (6x - 5) = 40 \) and verifying that both sides are equal.

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주요 개념

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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 on one side of the equation to find its value.

Distributive Property

The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. This property allows us to eliminate parentheses in expressions by distributing the multiplier across the terms inside the parentheses. In the context of the given equation, it helps simplify expressions like 6x - 5.

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.