Question

Solve for x 3x + 1 ≤2-x< 18+ 7x

Answer 1

X can be any number greater than -2 and less than or equal to 1/4.

Explanation:

To solve for x in the inequality 3x + 1 ≤ 2 - x < 18 + 7x, we will first isolate the variable x on one side of the inequality.

3x + 1 ≤ 2 - x

Adding x to both sides, we get:

4x + 1 ≤ 2

Subtracting 1 from both sides, we get:

4x ≤ 1

Dividing both sides by 4, we get:

x ≤ 1/4

Next, we solve the second inequality:

2 - x < 18 + 7x

Adding x to both sides, we get:

2 < 18 + 8x

Subtracting 18 from both sides, we get:

-16 < 8x

Dividing both sides by 8, we get:

-2 < x

Therefore, the solution to the inequality 3x + 1 ≤ 2 - x < 18 + 7x is:

-2 < x ≤ 1/4

This means that x can be any number greater than -2 and less than or equal to 1/4.

Answer 2

To solve for x, we first need to isolate x on one side of the inequality.

3x + 1 ≤ 2 - x < 18 + 7x

Add x to both sides of the inequality:

4x + 1 ≤ 2 < 18 + 6x

Subtract 1 from all sides:

4x ≤ 1 < 18 + 6x

Subtract 6x from all sides:

-2x ≤ 1 < 18

Divide all sides by -2. Since we are dividing by a negative number, we need to reverse the direction of the inequality:

-2x ≥ -9 and -2x < -1

Simplify:

x ≤ 4.5 and x > 0.5

Therefore, the solution is 0.5 < x ≤ 4.5.