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Unit 2: Solving equations & inequalities
About this unit.
There are lots of strategies we can use to solve equations. Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions.
Linear equations with variables on both sides
- Why we do the same thing to both sides: Variable on both sides (Opens a modal)
- Intro to equations with variables on both sides (Opens a modal)
- Equations with variables on both sides: 20-7x=6x-6 (Opens a modal)
- Equation with variables on both sides: fractions (Opens a modal)
- Equation with the variable in the denominator (Opens a modal)
- Equations with variables on both sides Get 3 of 4 questions to level up!
- Equations with variables on both sides: decimals & fractions Get 3 of 4 questions to level up!
Linear equations with parentheses
- Equations with parentheses (Opens a modal)
- Reasoning with linear equations (Opens a modal)
- Multi-step equations review (Opens a modal)
- Equations with parentheses Get 3 of 4 questions to level up!
- Equations with parentheses: decimals & fractions Get 3 of 4 questions to level up!
- Reasoning with linear equations Get 3 of 4 questions to level up!
Analyzing the number of solutions to linear equations
- Number of solutions to equations (Opens a modal)
- Worked example: number of solutions to equations (Opens a modal)
- Creating an equation with no solutions (Opens a modal)
- Creating an equation with infinitely many solutions (Opens a modal)
- Number of solutions to equations Get 3 of 4 questions to level up!
- Number of solutions to equations challenge Get 3 of 4 questions to level up!
Linear equations with unknown coefficients
- Linear equations with unknown coefficients (Opens a modal)
- Why is algebra important to learn? (Opens a modal)
- Linear equations with unknown coefficients Get 3 of 4 questions to level up!
Multi-step inequalities
- Inequalities with variables on both sides (Opens a modal)
- Inequalities with variables on both sides (with parentheses) (Opens a modal)
- Multi-step inequalities (Opens a modal)
- Using inequalities to solve problems (Opens a modal)
- Multi-step linear inequalities Get 3 of 4 questions to level up!
- Using inequalities to solve problems Get 3 of 4 questions to level up!
Compound inequalities
- Compound inequalities: OR (Opens a modal)
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- A compound inequality with no solution (Opens a modal)
- Double inequalities (Opens a modal)
- Compound inequalities examples (Opens a modal)
- Compound inequalities review (Opens a modal)
- Solving equations & inequalities: FAQ (Opens a modal)
- Compound inequalities Get 3 of 4 questions to level up!
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MathPapa Practice
MathPapa Practice has practice problems to help you learn algebra.
Basic Arithmetic
Subtraction, multiplication, basic arithmetic review, multi-digit arithmetic, addition (2-digit), subtraction (2-digit), multiplication (2-digit by 1-digit), division (2-digit answer), multiplication (2-digit by 2-digit), multi-digit division, negative numbers, addition: negative numbers, subtraction: negative numbers, multiplication: negative numbers, division: negative numbers, order of operations, order of operations 1, basic equations, equations: fill in the blank 1, equations: fill in the blank 2, equations: fill in the blank 3 (order of operations), fractions of measurements, fractions of measurements 2, adding fractions, subtracting fractions, adding fractions: fill in the blank, multiplication: fractions 1, multiplication: fractions 2, division: fractions 1, division: fractions 2, division: fractions 3, addition (decimals), subtraction (decimals), multiplication 2 (example problem: 3.5*8), multiplication 3 (example problem: 0.3*80), division (decimals), division (decimals 2), percentages, percentages 1, percentages 2, chain reaction, balance arithmetic, number balance, basic balance 1, basic balance 2, basic balance 3, basic balance 4, basic balance 5, basic algebra, basic algebra 1, basic algebra 2, basic algebra 3, basic algebra 4, basic algebra 5, algebra: basic fractions 1, algebra: basic fractions 2, algebra: basic fractions 3, algebra: basic fractions 4, algebra: basic fractions 5.
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Exercise 15 Page 389
Recall that (f± g)(x)=f(x)± g(x), (f* g)(x)=f(x)* g(x), and ( fg)(x)= f(x)g(x).
Check the answer
Practice exercises, asses your skill.
We want to perform arithmetic operations with the functions f(x) and g(x). To do so, we will calculate (f+g)(x), (f-g)(x), (f* g)(x), and ( fg)(x) separately.
Calculating (f+g)(x)
f(x)= 3x^2-4, g(x)= x^2-8x+4
Remove parentheses
Add and subtract terms
Calculating (f-g)(x)
Distribute -1
Calculating (f* g)(x)
Distribute (x^2-8x+4)
Distribute 3x^2
Distribute - 4
Subtract term
Calculating ( fg)(x)
Substitute values
Calculate power
Subtract terms
Split into factors
sqrt(a* b)=sqrt(a)*sqrt(b)
Calculate root
Factor out 2
a/b=.a /2./.b /2.
Geometry: Common Core (15th Edition)
By charles, randall i., chapter 1 - tools of geometry - 1-7 midpoint and distance in the coordinate plane - practice and problem-solving exercises - page 54: 6, work step by step, update this answer.
You can help us out by revising, improving and updating this answer.
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