solve te compound inequality
6 > -5x + 5 or 9 < - 3x + 4
Simplify both inequalities.
6 > -5x + 5
1 > -5x
5x > -1
x > -0.2
9 < -3x + 4
5 < -3x
3x < -5
x < -5/3
Final answer:
No solution
If x > -0.2, it cannot be also less than -5/3
rewrite as
5x > -1 OR 3x < -5
x > -1/5 OR x < -5/3
On a number line, draw a small open circle around -5/3 with an arrow on a line going to the left, and a small open circle around -1/5 with an arrow going to the right.
In other words, the only numbers that will NOT work are between -5/3 and -1/5 inclusive.
To solve the compound inequality 6 > -5x + 5 or 9 < -3x + 4, we need to solve each inequality separately and then combine the solutions.
Let's first solve the inequality 6 > -5x + 5:
1. Subtract 5 from both sides of the inequality:
6 - 5 > -5x + 5 - 5
1 > -5x
2. Divide both sides of the inequality by -5. Note that when you divide by a negative number, the direction of the inequality sign flips:
1 / -5 < -5x / -5
-1/5 < x
So, the solution to the first inequality is x > -1/5.
Now, let's solve the inequality 9 < -3x + 4:
1. Subtract 4 from both sides of the inequality:
9 - 4 < -3x + 4 - 4
5 < -3x
2. Divide both sides of the inequality by -3. Once again, since we are dividing by a negative number, the direction of the inequality sign flips:
5 / -3 > -3x / -3
-5/3 > x
Therefore, the solution to the second inequality is x < -5/3.
To combine the solutions, we take the intersection of the solutions to both inequalities. In other words, we need to find the values of x that satisfy both x > -1/5 and x < -5/3.
Graphically, the solution would be the values of x that fall between -5/3 and -1/5 on the number line, excluding -5/3 and -1/5.
In interval notation, the solution would be (-∞, -5/3) ∪ (-1/5, ∞).