(2)/(3)(p+3)>(5)/(6)(p-4)

Name: Problem 63, Chapter 2: Beginning and Intermediate Algebra
Uploaded: 2022-02-16T14:12:05-08:00
Duration: 3 min 44 s
Channel: Leslie Deeb
Description: (2)/(3)(p+3)>(5)/(6)(p-4)

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Key Concepts

Isolating the Variable

Isolating the variable involves performing algebraic operations to get the variable on one side of the inequality. This process includes combining like terms, clearing fractions, and performing inverse operations, and it is crucial for finding the solution to a linear inequality.

Linear Inequalities

Linear inequalities are mathematical expressions involving a linear function where two expressions are compared using inequality signs (>, <, ?, or ?). They follow similar steps to linear equations but require careful treatment of the inequality direction when multiplying or dividing by negative numbers.

Distributive Property

The distributive property is a key algebraic concept used to expand expressions by multiplying each term inside a parenthesis by the term outside. This property helps in rewriting expressions into simpler forms, which is essential for solving equations or inequalities.

Operations with Fractions

Operations with fractions are important in algebra because they allow the manipulation and simplification of expressions that contain fractional coefficients. Mastery of adding, subtracting, multiplying, and dividing fractions is necessary to solve equations and inequalities that involve fractional expressions.

Transcript

00:01 Let's look at how to solve this inequality.

00:04 On first glance, you might think that you would like to distribute.

00:08 However, distributing is just going to make four fractions instead of two.

00:14 And that's definitely the hardest part of this problem.

00:17 So instead, let's look at a way to clear the fractions.

00:22 I need the least common multiple of three and six, my current denominators.

00:30 To do that, i'm thinking about the numbers.

00:32 I say when i count by threes, and the numbers i say when i count by sixes, and the smallest number they have in common is six.

00:43 So if i multiply both sides of the equation by six, the fractions should disappear.

00:52 So times six here, times six here.

00:59 And what happens is, if i multiply straight across, on the left -hand side, this becomes 12 over 3, which is 4.

01:11 And on the right hand side, i get 30 over 6, which is 5.

01:21 And now that those fractions are gone, i have a much easier problem to deal with.

01:25 So now i will distribute.

01:28 So if i distribute the 4 here and here, remember distributing is multiplying, i get 4p plus 12 is greater then and i distribute on the right and i get 5p minus 20.

01:50 Next we're going to get our letters on the left.

01:54 So i'm going to move this 5p to the other side...

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