4x7<11 or 1-x<=-2 compound inequalities
first step:
what does 4x7 mean?
sorry I wrote it wrong
it is
4x+7<11 or 1-x<=-2
To solve the compound inequalities 4x7<11 and 1-x<=-2, we need to solve each inequality separately and then find the intersection of the solution sets.
1) 4x+7<11:
To solve this inequality, you need to isolate the variable x. Start by subtracting 7 from both sides:
4x < 11 - 7
4x < 4
Now, divide both sides by 4 (since 4 is positive, we do not need to change the direction of the inequality):
x < 1
So, the solution to the inequality 4x+7<11 is x < 1.
2) 1-x <= -2:
To solve this inequality, you need to isolate the variable x. Start by subtracting 1 from both sides:
1 - 1 - x <= -2 - 1
-x <= -3
Next, multiply both sides by -1 (since we are multiplying by a negative number, we need to reverse the direction of the inequality):
x >= 3
So, the solution to the inequality 1-x <= -2 is x >= 3.
Now, we find the intersection of the solution sets of the two inequalities by looking for values of x that satisfy both conditions simultaneously. Since there is no overlap between x < 1 and x >= 3, there is no solution to the compound inequalities 4x+7<11 and 1-x<=-2.