I need help with solving these absolute value inequalities. I have to graph them as well.
y< |x+2|+4
and
y>|x+5|+3
I just don't know what to do without a coefficient in front of the absolute value!
the coefficient is there. It is 1.
to see the graphs, go to wolframalpha.com and enter
plot y=|x+2|+4 and y=|x+5|+3
you want the area below the blue line and above the purple line.
To solve and graph absolute value inequalities, follow these steps:
Step 1: Set up two cases.
In case 1, drop the absolute value symbols and solve as if they were parentheses:
y< x + 2 + 4
In case 2, add a negative sign to the expression inside the absolute value:
y< -(x + 2) + 4
Step 2: Simplify the expressions.
Case 1:
y< x + 6
Case 2:
y< -x - 2 + 4
y< -x + 2
Step 3: Graph each case separately.
For case 1, since y < x + 6, graph a dashed line (because it's not an equal sign) with a slope of 1 and y-intercept of 6.
For case 2, since y < -x + 2, graph a dashed line (because it's not an equal sign) with a slope of -1 and y-intercept of 2.
Step 4: Determine the solutions.
For y< x + 6, shade the entire region below the line.
For y< -x + 2, shade the entire region below the line.
Step 5: Identify the overlap.
On the graph, locate the region where both cases overlap. This region represents the combined solution to the absolute value inequality.
That's it! You have now solved and graphed the absolute value inequalities.