Solve the compound inequality graph solution 6x-4<-34 or3x+10>10
6x-4<-34 or 3x+10>10
6x-4<-34
6x < -30
x < -5
or
3x+10>10
3x > 0
x > 0
You can see the solution graphed at
http://www.wolframalpha.com/input/?i=6x-4%3C-34+or+3x%2B10%3E10
To solve the compound inequality 6x - 4 < -34 or 3x + 10 > 10, we'll start by solving each inequality separately and then combining the solutions.
Let's solve the first inequality, 6x - 4 < -34:
Step 1: Add 4 to both sides of the inequality to isolate the variable:
6x - 4 + 4 < -34 + 4
6x < -30
Step 2: Divide both sides of the inequality by 6 to solve for x:
(6x)/6 < (-30)/6
x < -5
Now let's solve the second inequality, 3x + 10 > 10:
Step 1: Subtract 10 from both sides of the inequality to isolate the variable:
3x + 10 - 10 > 10 - 10
3x > 0
Step 2: Divide both sides of the inequality by 3 to solve for x:
(3x)/3 > (0)/3
x > 0
Now that we have solved each inequality separately, let's combine the solutions.
The compound inequality 6x - 4 < -34 or 3x + 10 > 10 can be written as two separate inequalities:
x < -5 or x > 0
To graph this compound inequality on a number line, we'll plot two separate graphs for each inequality and then combine them.
First, graph x < -5:
Draw an open circle at -5, and shade the line to the left of -5 since the solution is all real numbers less than -5.
Next, graph x > 0:
Draw an open circle at 0, and shade the line to the right of 0 since the solution is all real numbers greater than 0.
Combining the two graphs, the compound inequality is represented by the shaded region to the left of -5 and to the right of 0 on the number line.