7X+4>-13 or 9x+4>-23
The solution of the compound inequality is ? I am totally lost!!!!!!!!
All you have to do is solve each inequality, then pick all values for x that satisfy either one.
7x+4 > -13
7x > -17
x > -17/7
9x+4 > -23
9x > -27
x > -3
So, any x that is greater than -17/7, or which is greater than -3, solves the problem. Now, since -17/7 > -3, any value > -17/7 also satisfies the 2nd inequality.
So, the final solution is x > -3. Any value above -3 satisfies one or the other inequality. If you graph the intervals on the number line, you'll see they overlap.
Do I use the [ ] or the () on the number line?
To solve this compound inequality, you need to find the values of x that satisfy either or both of the inequalities. Here's how you can solve it step by step:
1. Start with the first inequality: 7x + 4 > -13. To isolate x, subtract 4 from both sides: 7x > -17.
2. Divide both sides of the inequality by 7 to solve for x: x > -17/7.
Now, move on to the second inequality: 9x + 4 > -23.
3. Subtract 4 from both sides: 9x > -27.
4. Divide both sides of the inequality by 9: x > -27/9.
Now, you have two separate solutions for x:
- x > -17/7 (from the first inequality)
- x > -27/9 (from the second inequality)
To determine the solution of the compound inequality, you need to find the overlapping region between these two solutions.
Considering both inequalities, x must be greater than both -17/7 and -27/9.
To find the common region, look for the larger value between -17/7 and -27/9. In this case, -17/7 is larger than -27/9.
Therefore, the solution is x > -17/7. This means any value of x that is greater than -17/7 will satisfy the compound inequality.
In conclusion, the solution of the compound inequality is x > -17/7.