Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. R - Algebra Review

Problem R.2.125

Chapter 1, Problem R.2.125

Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 7r - 9r

Verified step by step guidance

Identify the common factor in the terms of the expression. Here, both terms have the variable \( r \).

Use the distributive property, which states that \( a b + a c = a(b + c) \), to factor out the common \( r \) from both terms: \( 7r - 9r = r(7 - 9) \).

Simplify the expression inside the parentheses by performing the subtraction: \( 7 - 9 \).

Rewrite the expression as \( r \) multiplied by the simplified result from the previous step.

If possible, write the final simplified expression by multiplying \( r \) by the simplified number.

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.

Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend individually and then adding the products. In algebra, it is expressed as a(b + c) = ab + ac, allowing simplification of expressions by factoring or expanding.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, 7r and -9r are like terms because both contain the variable r, so they can be combined by performing the arithmetic operation on their coefficients.

Simplification of Algebraic Expressions

Simplification means rewriting an expression in its simplest form by performing all possible operations. This includes applying properties like distributive property and combining like terms to reduce the expression to a more manageable or recognizable form.

Recommended video:

6:36

Simplifying Trig Expressions

Related Practice

Textbook Question

Fill in the blank(s) to correctly complete each sentence.

To graph the function ƒ(x) = x² - 3, shift the graph of y = x² down ___ units.

views

Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. 5 + √3 is a real number.

Textbook Question

CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The set containing no elements is the _______, symbolized _______.

Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. 3p - 2r

views

Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. (q + r)/ (q + p)

views

Textbook Question

CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The point (4, ________) lies on the graph of the equation y = 3x - 6.

views