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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)
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- Equations with variables on both sides Get 3 of 4 questions to level up!
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## Linear equations with parentheses

- Equations with parentheses (Opens a modal)
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- Equations with parentheses Get 3 of 4 questions to level up!
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## 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)
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## Linear equations with unknown coefficients

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## Multi-step inequalities

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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.

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