Question

Solve the inequality. (Lesson 5.7)

$-\frac{5}{9}x+1>\frac{22}{7}$

Short answer

The solution is$x<-\frac{135}{35}.$

Step-by-step solution

Step 1.  Given

The given inequality is$-\frac{5}{9}x+1>\frac{22}{7}.$

Step 2.  To determine

We have to solve the inequality$-\frac{5}{9}x+1>\frac{22}{7}.$

Step 3.  Calculation 

Solve the given inequality.

$\begin{array}{c}-\frac{5}{9}x+1>\frac{22}{7}\\ \frac{-5x+9}{9}\text{>}\frac{22}{7}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}[}\because \text{TakingLeastcommonfactor]}\\ \left(-5x+9\right)·7\text{>}22·9\\ -35x+63>198\\ -35x+63-63>198-63\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}[}\because \text{Subtracting63onbothsides]}\\ -35x>135\\ x<-\frac{135}{35}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}[}\because \text{Dividing-35onbothsidesandreversingtheinequalitysign]}\end{array}$

Hence, $x<-\frac{135}{35}$ is the required solution.