Question

Solve each open sentence.

x29+x110=0\frac { x ^ { 2 } } { 9 } + \frac { x - 1 } { 10 } = 0

Solution

Verified
Step 1
1 of 2

90(x29+x110)=900Multiply both sides by 90,the LCM of 9, and 10.90x29+90x110=0Use the Distributive Property.10x2+9(x1)=0Simplify.10x2+9x9=0Use the Distributive Property.(5x3)(2x+3)=0\begin{align*} 90 \cdot\left(\frac{x^2}{9}+\frac{x-1}{10}\right)&=90 \cdot 0 && \text{Multiply both sides by} \ 90, \\ &\text{} && \text{the LCM of} \ 9, \ \text{and} \ 10. \\ 90 \cdot \frac{x^2}{9}+90 \cdot \frac{x-1}{10}&=0 && \text{Use the Distributive Property.} \\ 10x^2+9 \cdot \left(x-1\right)&=0 && \text{Simplify.} \\ 10x^2+9x-9&=0 && \text{Use the Distributive Property.} \\ \left(5x-3\right)\left(2x+3\right)&=0 \\ \end{align*}

The given equation already has 00 as one side, and the other side is already factored. Simply set each factor equal to 00 and solve:

(5x3)=0or(2x+3)=0Zero-Product Property5x=3or2x=3x=35orx=32\begin{align*} \left(5x-3\right)&=0 \hspace{1cm} \text{or} \hspace{1cm} \left(2x+3\right)=0 \hspace{2cm} \text{Zero-Product Property} \\ 5x&=3 \hspace{1cm} \text{or} \hspace{2cm} 2x=-3 \\ x&=\frac{3}{5} \hspace{1cm} \text{or} \hspace{2.2cm} x=-\frac{3}{2} \\ \end{align*}

The solution set is {35,32}\boxed{\color{#c34632}\left\lbrace \frac{3}{5}, -\frac{3}{2}\right\rbrace}

Create a free account to view solutions

Create a free account to view solutions

Recommended textbook solutions

enVision Algebra 2 1st Edition by Al Cuoco

enVision Algebra 2

1st EditionISBN: 9780328931590Al Cuoco
3,573 solutions
Algebra and Trigonometry: Structure and Method, Book 2 1st Edition by Brown, Dolciani, Kane, Sorgenfrey

Algebra and Trigonometry: Structure and Method, Book 2

1st EditionISBN: 9780395977255 (2 more)Brown, Dolciani, Kane, Sorgenfrey
8,447 solutions
Big Ideas Math Algebra 2: A Common Core Curriculum 1st Edition by Boswell, Larson

Big Ideas Math Algebra 2: A Common Core Curriculum

1st EditionISBN: 9781608408405 (1 more)Boswell, Larson
5,307 solutions
Big Ideas Math: Algebra 2 A Common Core Curriculum 1st Edition by Laurie Boswell, Ron Larson

Big Ideas Math: Algebra 2 A Common Core Curriculum

1st EditionISBN: 9781642088052Laurie Boswell, Ron Larson
5,307 solutions

More related questions

1/4

1/7