Pregunta
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
All real numbers
less than
.
Solución
To solve the inequality
and graph the solution, follow these steps:
Step 1: Simplify the Inequality
Start by simplifying the right-hand side of the inequality.
Distribute the negative sign inside the parentheses:
Combine like terms (
):
Step 2: Isolate the Variable Term
Add 3 to both sides to move the constant term to the left side:
Step 3: Solve for
Divide both sides by 16 to isolate
:
Simplify the fraction:
This can also be written as:
Step 4: Graph the Solution
To graph the solution
on a number line:
- Draw a number line with relevant points, including
. - Place an open circle at
to indicate that is not included in the solution (since the inequality is strictly “<”). - Shade the region to the left of
to represent all real numbers less than .
Here is a visual representation:
<----|----------|----------|----------|---->
0 1/2 1 3/2
●---------------->
- ● represents the open circle at
. - The arrow pointing to the left indicates all values less than
.
Final Answer
All real numbers
less than
.
Graph of the Solution

(In the graph, an open circle is placed at
with shading extending to the left.)
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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The Deep Dive
To solve the inequality
, let’s first simplify the right side. Distributing the negative sign gives us
. Combining like terms results in
. Now, add 3 to both sides:
Dividing both sides by 16 gives you
, or
.
To graph the solution, draw a number line and place a circle at
with a line extending to the left, indicating all values of
that are less than
.
Combine those concepts, and voilà! You’ve not only got the solutions but a nice visual too!
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