can someone help in solving this and use set builder notations to describe the solution Please
4(8-2x)+2x<5(9+3x)
4(8-2x)+2x<5(9+3x)
32 - 8x + 2x < 45 + 15x
32 - 6x < 45 + 15x
-21x < 13
When dividing by a neg number,
the sense of the inequality is reversed
x > -13/21
Can you show me the step by step to solve -3(4y-2)<30?
To solve the inequality equation
4(8 - 2x) + 2x < 5(9 + 3x),
we'll start by simplifying both sides:
32 - 8x + 2x < 45 + 15x.
Combine like terms on both sides:
32 - 6x < 45 + 15x.
Now, let's isolate the x variable on one side of the inequality.
First, we'll subtract 32 from both sides:
-6x < 13 + 15x.
Next, we'll subtract 15x from both sides:
-21x < 13.
To solve for x, divide both sides by -21. However, we need to be cautious when dividing by a negative number because it flips the inequality sign:
x > 13 / -21 (remember to flip the inequality sign since we divided by a negative number).
Simplifying the right side:
x > -13/21.
Now, we can express the solution using set builder notation.
The solution set can be represented as {x | x > -13/21}, which reads "the set of x such that x is greater than -13/21".