Table of contents

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1. Review of Real Numbers1h 33m

Evaluating Exponents
15m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Simplifying Expressions
44m

2. Linear Equations and Inequalities5h 35m

Solving Linear Equations
2h 23m

Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
1h 7m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

3. Solving Word Problems2h 39m

Introduction to Problem Solving
37m

Formulas
25m

Percent Problem Solving
59m

Mixture Problem Solving
37m

4. Graphs and Functions2h 48m

The Rectangular Coordinate System
27m

Graph Linear Equations Using Intercepts
11m

Slope of a Line
33m

Slope-Intercept Form
25m

Point Slope Form
13m

Introduction to Relations and Functions
25m

Function Notation
15m

Composition of Functions
17m

5. Systems of Linear Equations1h 12m

Solving Systems of Linear Equations by Graphing
29m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
27m

6. Exponents, Polynomials, and Polynomial Functions1h 27m

The Product Rule
9m

The Quotient Rule
10m

Intro to the Power Rules
17m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
5m

Multiplying Polynomials
38m

7. Factoring1h 30m

Factoring by Greatest Common Factor & Grouping
26m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Quadratic Equations & Applications
14m

8. Rational Expressions and Functions2h 21m

Simplifying Rational Expressions
33m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

9. Roots, Radicals, and Complex Numbers2h 33m

Introduction to Radical Expressions
11m

Simplifying Radical Expressions
27m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
23m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

10. Quadratic Equations and Functions1h 23m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
31m

11. Inverse, Exponential, & Logarithmic Functions1h 5m

Introduction to Inverse Functions
25m

Exponential Functions
13m

Introduction to Logarithmic Functions
26m

12. Conic Sections & Systems of Nonlinear Equations58m

Graphing Circles
32m

Ellipses
15m

Parabolas
10m

13. Sequences, Series, and the Binomial Theorem1h 21m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Factorials
13m

2. Linear Equations and Inequalities

Solving Linear Equations

Intermediate Algebra

2. Linear Equations and Inequalities

Solving Linear Equations

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Multiple Choice

How many solutions does each of the following equations have?
$4 (x - 3) = 4 x - 12$

One solution

Infinite solutions

No solution

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Verified step by step guidance

Start by expanding the left side of the equation \$4\left(x - 3\right) = 4x - 12$ using the distributive property: multiply 4 by each term inside the parentheses.

After expansion, rewrite the equation in the form \$4x - 12 = 4x - 12$.

Next, observe both sides of the equation to see if they are identical expressions or if they differ.

If both sides are identical for all values of $x$, this means the equation has infinitely many solutions.

If the expressions were different and could not be made equal, the equation would have no solution; if they were equal for only specific values of $x$, it would have one solution.