solve this two sided inequality 7<1-2x<-10
* i think your inequality is your because -10 cannot be greater than 7,, anyway, solving for x:
7 < 1-2x < -10
7-1 < -2x < -10-1
6 < -2x < -11
-3 > x > 11/2
*note that when you divide a negative number (here, we divide -2 to all terms to get x), you must reverse the signs of inequality,,
..i think the given inequality must be
7 > 1-2x > -10
so that you would obtain:
-3 < x < 11/2
because -3 cannot be greater than 11/2
so there,, :)
Solve the two sided inequality and show the solution on real line
7 < 1-2x ≤ 10
-1<1/x < 1
To solve the two-sided inequality 7 < 1 - 2x < -10, we need to isolate the variable x. Let's break it down into two separate inequalities and solve them individually:
1. 7 < 1 - 2x:
Subtract 1 from both sides of the inequality:
7 - 1 < 1 - 1 - 2x
6 < -2x
Divide both sides by -2, remembering that when dividing or multiplying by a negative number, we flip the inequality sign:
6 / -2 > -2x / -2
-3 > x
Therefore, the solution for the first inequality is x < -3.
2. 1 - 2x < -10:
Subtract 1 from both sides of the inequality:
1 - 1 - 2x < -10 - 1
-2x < -11
Divide both sides by -2, remembering to flip the inequality sign:
-2x / -2 > -11 / -2
x > 11/2 or x > 5.5
Therefore, the solution for the second inequality is x > 5.5.
Combining the two solutions, we have -3 < x < 5.5 as the solution to the original two-sided inequality 7 < 1 - 2x < -10.