solve each inequality or equation. Graph the solution.
5(absolute value 3w+2)-3>7
*Please show me the work
To solve the inequality 5|3w+2| - 3 > 7, follow these steps:
Step 1: First, isolate the absolute value term by adding 3 to both sides of the inequality:
5|3w+2| > 10
Step 2: Divide both sides of the inequality by 5 to get rid of the coefficient:
|3w+2| > 2
Step 3: Since |3w+2| represents the distance between 3w+2 and zero on the number line, the inequality |3w+2| > 2 can be rewritten as two separate inequalities:
3w+2 > 2 or 3w+2 < -2
Step 4: Solve each inequality separately:
For the first inequality 3w+2 > 2:
Subtract 2 from both sides:
3w > 0
Divide both sides by 3:
w > 0
For the second inequality 3w+2 < -2:
Subtract 2 from both sides:
3w < -4
Divide both sides by 3:
w < -4/3
Step 5: Now we have two separate solutions, w > 0 and w < -4/3. To graph the solution, plot a number line and mark the critical points, which are 0 and -4/3.
-4/3 0
--------------------o------------->
Step 6: Shade the region on the number line that satisfies the inequality. Since w should be greater than 0, shade the line to the right of 0, and since w should be less than -4/3, shade the line to the left of -4/3.
-4/3 0
----o=======================>
This graph represents the solution to the inequality 5|3w+2| - 3 > 7, where w > 0 and w < -4/3.