4/3 s -3 <s+ 2/3-1/3s
To solve this inequality, let's simplify and combine like terms:
4/3s - 3 < s + 2/3 - 1/3s
Multiplying through by 3 to eliminate the fractions:
4s - 9 < 3s + 2 - s
Combine like terms:
4s - 9 < 2s + 2
Subtract 2s from both sides:
2s - 9 < 2
Add 9 to both sides:
2s < 11
Divide by 2:
s < 11/2
Therefore, the solution to the inequality is s < 11/2.
To solve the inequality 4/3 s - 3 < s + 2/3 - 1/3s, we will simplify and isolate the variable s step by step.
1. Start by simplifying both sides of the inequality:
4/3 s - 3 < s + 2/3 - 1/3s
Multiply through by 3 to eliminate the fractions:
4s - 9 < 3s + 2 - s
2. Combine like terms on each side of the inequality:
4s - 9 < 3s + 2 - s
4s - 9 < 2s + 2
3. Move all terms involving s to the left side and the constants to the right side:
4s - 2s < 9 + 2
2s < 11
4. Divide both sides by 2 to solve for s:
2s/2 < 11/2
s < 11/2
Thus, the solution to the inequality is s < 11/2.
To solve the inequality, we need to isolate the variable 's'. Here's the step-by-step explanation:
1. Distribute the fractions on both sides of the inequality:
4/3 s - 3 < s + 2/3 - 1/3s.
Multiply 4/3 by s to get (4/3)s, multiply 1/3 by s to get (1/3)s, and multiply 2/3 by 1 to get 2/3.
The inequality becomes:
(4/3)s - 3 < s + 2/3 - (1/3)s.
2. Group the 's' terms on one side and the constant terms on the other side:
To do this, add (1/3)s to both sides of the inequality:
(4/3)s - (1/3)s - 3 + (1/3)s < s + (1/3)s + 2/3 - (1/3)s.
Simplifying the equation gives:
(4/3)s - (1/3)s - 3 + (1/3)s < s + (1/3)s + 2/3.
3. Combine like terms:
On the left side of the inequality, (1/3)s and -(1/3)s cancel each other out, leaving us with:
(4/3)s - (1/3)s = (3/3)s = s.
On the right side of the inequality, s and -(1/3)s cancel each other out, leaving us with:
s + (1/3)s = (4/3)s.
Similarly, -3 and 2/3 combine to give us -7/3.
The inequality becomes:
s - 7/3 < (4/3)s + 2/3.
4. Move the (4/3)s term to the left side by subtracting (4/3)s from both sides:
s - (4/3)s - 7/3 < (4/3)s - (4/3)s + 2/3.
Simplifying the equation gives:
-(1/3)s - 7/3 < 2/3.
5. Add 7/3 to both sides to isolate the (-1/3)s term:
-(1/3)s - 7/3 + 7/3 < 2/3 + 7/3.
Simplifying the equation gives:
-(1/3)s < 9/3.
-(1/3)s < 3.
6. To solve for 's', we need to multiply both sides of the inequality by -3. However, when multiplying or dividing an inequality by a negative number, we need to flip the inequality sign:
Multiplying both sides by -3 gives:
-(1/3)s * -3 > 3 * -3.
Simplifying the equation gives:
s > -9.
Therefore, the solution to the inequality 4/3 s - 3 < s + 2/3 - 1/3s is s > -9.