Question

Solve the inequality. Graph the solution on the number line and write the solution in the interval notation.

$9y+5\left(y+3\right)<4y-35$

Short answer

$y<-5$

$\left(-\infty ,-5\right)$

Step-by-step solution

Step 1. Given information.

The given inequality is

$9y+5\left(y+3\right)<4y-35$

Step 2. Solving the inequality.

Distribute and combine like terms:

$9y+5y+15<4y-35$

$14y+15<4y-35$

Subtracting $4y+15$from both sides and simplifying:

$14y+15-4y-15<4y-35-4y-15$

$10y<-50$

Diving both sides by 10 and simplifying:

$\frac{10y}{10}<\frac{-50}{10}$

$y<-5$

The solution to the inequality is$y<-5$

Step 3. Graphing the solution on the number line.

The graph of the solution on the number line is presented below:

Step 4. Writing the solution in the interval notation.

The solution in the interval notation can be expressed as

$\left(-\infty ,-5\right)$