Solve. 4a-2≤a+1≤3a+4

4a-2-1≤a+1-1≤3a+4-1
4a-3-3≤a≤3a+3-3
4a/3-6/3≤a≤3a/3
4a/3(1/a)-2≤a≤a(1/a)
4/3-6≤a≤1
I got lost at this part. I'm not sure what to do now, if i am solving it correctly.

Solve. 3x<4-5x<5+3x
3x<4-4-5x<5-4+3x
3x/3x<-5x<1+3x/3x
I was not sure where to go from here. This is most likely incorrect, the way I am solving it.

4a-2 ≤ a+1 ≤ 3a+4

4a-2 ≤ a+1 AND a+1 ≤ 3a+4
3a ≤ 3 AND -2a ≤ 3
a ≤ 1 AND a ≥ -3/2

so : -3/2 ≤ a ≤ 1

3x<4-5x<5+3x
0 < 4-8x < 5
-4 < -8x < 1
1/2 > x > -1/8
or
-1/8 < x < 1/2

the reason I did not have to split up the second is that we could subtract 3x from both ends and the x's disappeared.
I had to split up the first, since I could not eliminate the x's from both ends.

Thank you so much.

To solve inequalities, we need to isolate the variable on one side of the inequality symbol. Let's solve the first inequality:

4a - 2 ≤ a + 1 ≤ 3a + 4

First, let's simplify each side of the inequality separately:

4a - 2 - 1 ≤ a + 1 - 1 ≤ 3a + 4 - 1

Simplifying further,

4a - 3 ≤ a ≤ 3a + 3

Now, we can isolate the variable "a" in the middle:

4a - 3 - 3a ≤ a - 3a ≤ 3a + 3 - 3a

Combine like terms:

a - 3 ≤ 0 ≤ 3a

Next, we can simplify further by dividing each term by 3:

(a - 3)/3 ≤ 0 ≤ 3a/3

Simplifying,

(a - 3)/3 ≤ 0 ≤ a

Now, we have the solution for "a" in terms of inequality.

For the second inequality, let's solve it step by step:

3x < 4 - 5x < 5 + 3x

First, simplify each side separately:

3x < 4 - 5x < 5 + 3x

Now, let's focus on the left side:

3x < 4 - 5x

We can simplify it further by adding 5x to both sides:

3x + 5x < 4 - 5x + 5x

Combine like terms:

8x < 4

Next, divide both sides by 8:

(8x)/8 < 4/8

Simplify:

x < 1/2

For the right side of the inequality:

4 - 5x < 5 + 3x

Subtract 4 from both sides:

4 - 5x - 4 < 5 + 3x - 4

Combine like terms:

-5x < 1 + 3x

Next, subtract 3x from both sides:

-5x - 3x < 1 + 3x - 3x

Combine like terms:

-8x < 1

Finally, divide both sides by -8:

(-8x) / -8 > 1 / -8

Remember, when dividing (or multiplying) both sides by a negative number, the direction of the inequality sign flips:

x > -1/8

Therefore, the solution for the second inequality is x > -1/8.

I hope this helps!