Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

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2:04 minutes

Problem 7

Textbook Question

In Exercises 1–26, solve and check each linear equation.11x - (6x - 5) = 40

Verified step by step guidance

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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Key Concepts

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

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.