Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 40a

Chapter 2, Problem 40a

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - (x - 3)/2 = (x + 2)/3

Verified step by step guidance

Step 1: Identify the least common denominator (LCD) of all the denominators in the equation. The denominators are 5, 2, and 3. The LCD is 30.

Step 2: Multiply every term in the equation by the LCD (30) to eliminate the fractions. This means multiplying each term by 30 and simplifying.

Step 3: Distribute the multiplication across each term. For example, 30 * (3x/5) becomes (30 * 3x) / 5, which simplifies to 18x. Repeat this process for the other terms.

Step 4: After clearing the fractions, simplify the resulting equation by combining like terms and isolating the variable (x). This may involve distributing, combining terms, and moving terms across the equals sign.

Step 5: Solve for x by dividing or performing any necessary operations to isolate x completely. Check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Linear Equations

Linear equations are mathematical statements that express the equality of two linear expressions. They typically take the form ax + b = c, where a, b, and c are constants, and x is the variable. Understanding how to manipulate these equations is essential for solving them, as it involves isolating the variable on one side of the equation.

Common Denominator

When dealing with fractions in linear equations, finding a common denominator is crucial for simplifying the equation. The common denominator allows you to eliminate the fractions by multiplying each term by this value, making it easier to solve for the variable. This step is particularly important when the equation contains multiple fractions with different denominators.

Isolating the Variable

Isolating the variable is a key step in solving linear equations, where the goal is to get the variable (e.g., x) alone on one side of the equation. This often involves performing inverse operations, such as addition, subtraction, multiplication, or division, to both sides of the equation. Mastery of this concept is essential for finding the solution to the equation.

Recommended video:

Guided course

05:28

Equations with Two Variables

Related Practice

Textbook Question

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x squared minus 7 x$

Textbook Question

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x² + 3x

Textbook Question

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 1 - (x + 3) ≥ 4 - 2x

Textbook Question

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 2 + √-4)²

views

Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? E = mc² for m

Textbook Question

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. $(x^{2} - x - 4)^{\frac{3}{4}} - 2 = 6$

views