Question

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

$13q<7q-29$

Short answer

The solution to the inequality will be

$q<-\frac{29}{6}$

The graph of the inequality will be

The solution in the interval notation is$\left(-\infty ,-\frac{29}{6}\right)$

Step-by-step solution

Step 1. Given information.

The following inequality is given

$13q<7q-29$

Step 2. Finding the solution to the inequality.

Subtract $7q$from both sides of the inequality

$13q-7q<7q-29-7q$

Simplify

$6q<-29$

Dividing both sides of the inequality by 6. Since 6 is a positive number, the sign of inequality remains the same

$\frac{6q}{6}<\frac{-29}{6}$

Simplify

$q<-\frac{29}{6}$

So, the solution to the given inequality is

$q<-\frac{29}{6}$

Step 3. Graphing the solution on the number line.

The graph of the solution will be

Step 4. Writing the solution in the interval notation.

The solution in the interval notation can be expressed as

$\left(-\infty ,-\frac{29}{6}\right)$