Question

salgtrig5 1.8.014. solve the linear inequality. express the solution using interval notation. 5x + 19 < 4 graph the solution set. use the tools to enter your answer. webassign.numberline

Explanation:

Step1: Isolate the term with x

Subtract 19 from both sides of the inequality $5x + 19<4$.
$5x+19 - 19<4 - 19$
$5x<-15$

Step2: Solve for x

Divide both sides of the inequality $5x < - 15$ by 5. Since 5>0, the direction of the inequality sign remains the same.
$\frac{5x}{5}<\frac{-15}{5}$
$x < - 3$

Step3: Write in interval notation

The solution in interval notation is $(-\infty,-3)$.

Step4: Graph the solution set

On the number - line, we use an open circle at - 3 (because x is strictly less than - 3, not equal to - 3) and draw an arrow to the left to represent all the numbers less than - 3.

Answer:

Interval notation: $(-\infty,-3)$
Graph: Use an open - circle at $x = - 3$ and draw an arrow to the left on the number line.