How do you graph and solve #|1+x|

Question

How do you graph and solve #|1+x|<8#?

Savannah Anderson · Accepted Answer

# -9 < x < 7 #

We can graph this on a number line by placing hollow dots over #-9, 7# (to indicate they are not part of the solution) and connecting the two dots with a line segment.

We can approach this question this way: #abs(1+x)<8# #-8<1+x<8# # -9 < x < 7 # We can graph this on a number line by placing hollow dots over #-9, 7# (to indicate they are not part of the solution) and connecting the two dots with a line segment.

Savannah Anderson · Answer

undefined To graph and solve the inequality $ |1+x| < 8 $, follow these steps:

1. **Graphing:**
   Begin by graphing the function $ y = |1+x| $. This function is a "V" shape with its vertex at $(-1,0)$. It opens upwards and has a slope of 1 on both sides.
   
   Then, graph the horizontal line $ y = 8 $. This line represents the boundary of the solution set.

2. **Solving:**
   To solve the inequality, we need to find the values of $ x $ that make $ |1+x| $ less than 8.

First, consider the expression inside the absolute value:
   $ 1+x < 8 $ and $ -(1+x) < 8 $.

Solve each inequality separately:
   $ 1+x < 8 $ becomes $ x < 7 $.
   $ -(1+x) < 8 $ becomes $ -1 - x < 8 $, which simplifies to $ x > -9 $.

So, the solution to the inequality is $ -9 < x < 7 $.

3. **Plotting on the Graph:**
   On the graph, shade the area between the two vertical lines representing $ x = -9 $ and $ x = 7 $. This shaded region represents the solution set for the inequality $ |1+x| < 8 $.

How do you graph and solve #|1+x|&lt;8#?

How do you graph and solve #|1+x|<8#?