Math

QuestionSolve the inequality 3(x3)5(1x)-3(x-3) \leq 5(1-x). What is the solution for xx?

Studdy Solution

STEP 1

Assumptions1. We are solving the inequality 3(x3)5(1x)-3(x-3) \leq5(1-x). . We are looking for all xx that satisfy the inequality.

STEP 2

First, we need to distribute the - on the left side of the inequality and the 55 on the right side of the inequality.
x+955x-x +9 \leq5 -5x

STEP 3

Next, we need to get all the xx terms on one side of the inequality and the constants on the other side. We can do this by adding 5x5x to both sides and subtracting 99 from both sides.
3x+5x59-3x +5x \leq5 -9

STEP 4

implify the inequality.
2x42x \leq -4

STEP 5

Finally, we need to isolate xx by dividing both sides of the inequality by 22.
x2x \leq -2So, the solution to the inequality 3(x3)5(1x)-3(x-3) \leq5(1-x) is x2x \leq -2.

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