Write using set builder notation.Show work....Solve..-2(10x-9)-17x<(6-x)
-2(10x-9)-17x < (6-x).
-20x + 18 - 17x < 6 - x.
-20x - 17x + x < 6 - 18.
-36x < -12.
X > -12 / -36.
X > 1/3.
3x+3(x-1)<-18
To solve the inequality -2(10x-9)-17x < (6-x), let's break it down step by step:
Step 1: Distribute the -2 to the terms inside the parentheses on the left side of the equation:
-20x + 18 - 17x < 6 - x
Step 2: Combine like terms on both sides of the equation:
-20x - 17x + x < 6 - 18
Simplifying further:
-36x < -12
Step 3: Divide both sides of the inequality by the coefficient of x (-36) to isolate x:
(-36x) / -36 > (-12) / -36
Simplifying further:
x > 1/3
Therefore, the solution to the inequality -2(10x-9)-17x < (6-x) is x > 1/3.
In set-builder notation, we can represent the solution as {x | x > 1/3}.