Solve the inequality algebraically: -16 less than or = to 7-2x less than or = to 5.?

Answer 1

- 16 ≤ 7 - 2x gives:-
2x ≤ 7 + 16
2x ≤ 23
x ≤ 23/2

7 - 2x ≤ 5
2x ≥ 2
x ≥ 1

Solution is 1 ≤ x ≤ 23/2

Answer 2

Given: -16 ≤ 7 - 2x ≤ 5
1. Subtract 7 from the three sections of the inequality.
-16 - 7 ≤ -2x ≤ 5 - 7
- 23 ≤ -2x ≤ -2
2. Divide by -2.
(-23) / (-2) ≥ x ≥ (-2) / (-2)
23/2 ≥ x ≥ 1.

Since,
x ≥ 1
1 ≤ x
and
23/2 ≥ x
x ≤ 23/2
We can write 1 ≤ x ≤ 23/2.

Answer 3

-16 <= 7-2x <= 5

this is like regular alegbra, but whenever you changing something on one side, you have to do it to all sides of the inequality. first, subtract 7

-23 <= -2x <= -2

next, divide by -2 to solve for x. For inequalities, whenever you multiply or divide by a negative number, you have to switch the direction of the inequality.

11.5 >= x >= 1

Answer 4

-16 <= 7 - 2x <= 5
Subtract 7 from each side
-23 <= -2x <= -2
Divide all sides by -2 (remember to flip the inequality sign when dividing by a negative number)
-23/-2 >= x >= -2/-2
Simplify
23/2 >= x > 1

Answer 5

-16 < = 7 - 2x < = 5

-16 < = 7 - 2x
-23 < = -2x
23/2 > = x

7 - 2x < = 5
-2x < = -2
x > = 1

so 1< = x < = 23/2