Question

# Solve each open sentence.$\frac { x ^ { 2 } } { 9 } + \frac { x - 1 } { 10 } = 0$

Solution

Verified
Step 1
1 of 2

\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 $0$ as one side, and the other side is already factored. Simply set each factor equal to $0$ and solve:

\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 $\boxed{\color{#c34632}\left\lbrace \frac{3}{5}, -\frac{3}{2}\right\rbrace}$

## Recommended textbook solutions

#### enVision Algebra 2

1st EditionISBN: 9780328931590Al Cuoco
3,573 solutions

#### 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 EditionISBN: 9781608408405 (1 more)Boswell, Larson
5,307 solutions

#### Big Ideas Math: Algebra 2 A Common Core Curriculum

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