solve the compund inequality. 6>-4x+5 or 7≤-2x+4
6 > -4x + 5 7 ≤ -2x + 4
1 > -4x 3 ≤ -2x
1/4 < x x ≤ -3/2
6>-4x+5 or 7≤-2x+4
4x > -1 or 2x ≤ -3
x > -1/4 OR x ≤ -3/2
To solve the compound inequality 6 > -4x + 5 or 7 ≤ -2x + 4, we can solve each inequality separately and then combine the solutions.
Starting with the first inequality, 6 > -4x + 5, let's isolate the variable x:
6 > -4x + 5
2 > -4x (subtracting 5 from both sides)
-2/4 < x (dividing both sides by -4, and reversing inequality by multiplying by a negative number)
Therefore, the solution to the first inequality is x > -1/2.
Moving on to the second inequality, 7 ≤ -2x + 4, we'll again isolate x:
7 ≤ -2x + 4
3 ≤ -2x (subtracting 4 from both sides)
-3/2 ≥ x (dividing both sides by -2, and reversing inequality by multiplying by a negative number)
So, the solution to the second inequality is x ≤ -3/2.
Now, to determine the solution to the compound inequality, we need to combine the individual solutions. In this case, we have two separate inequalities:
x > -1/2 (from the first inequality)
x ≤ -3/2 (from the second inequality)
To find the overlapping solution, we can see that x has to satisfy both conditions simultaneously. It means the solution should be the interval where both conditions are true. So, the final solution is:
-3/2 ≤ x < -1/2
This means x is greater than or equal to -3/2 and less than -1/2.