two questions that i cannnnnnot get!:
2/3(t)-(2-3t)<5t+2(1-t)
and;
4[5x-(3x-7)]<2(4x-5)
please help!
Sure, I can help you solve both of these inequalities step by step. Let's start with the first one:
1) 2/3(t) - (2 - 3t) < 5t + 2(1 - t)
Step 1: Distribute the 2 in 2(1 - t) to get:
2/3(t) - 2 + 6t < 5t + 2 - 2t
Step 2: Simplify both sides of the inequality:
(2/3)t - 2 + 6t < 5t + 2 - 2t
(2/3)t + 6t - 5t + 2t < 2 + 2
Step 3: Combine like terms on both sides of the inequality:
(2/3 + 6 - 5 + 2)t < 4
Step 4: Simplify the equation:
(13/3)t < 4
Step 5: Divide both sides of the inequality by (13/3) to isolate t:
t < (4 / (13/3))
t < (4 * (3/13))
t < (12/13)
So, the solution to the first equation is t < 12/13.
Now let's move on to the second equation:
2) 4[5x - (3x - 7)] < 2(4x - 5)
Step 1: Simplify within the brackets:
4[5x - 3x + 7] < 2(4x - 5)
4[2x + 7] < 2(4x - 5)
Step 2: Distribute the 4 and 2 on each side of the inequality:
8x + 28 < 8x - 10
Step 3: Move the variables to one side and the constants to the other side of the inequality:
8x - 8x < -10 - 28
0 < -38
Step 4: Since 0 is always less than any negative number, this inequality has no solution. There is no value of x that satisfies the inequality.
In conclusion, the inequality 4[5x - (3x - 7)] < 2(4x - 5) has no solution.