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-6r-5(-10 r+6) <= 3r+9+2r

−6r−5(−10r+6)≤3r+9+2r -6 r-5(-10 r+6) \leq 3 r+9+2 r

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Full solution

Q. −6r−5(−10r+6)≤3r+9+2r -6 r-5(-10 r+6) \leq 3 r+9+2 r
  1. Distribute and Combine Terms: First, distribute the −5-5 into (−10r+6)(-10r+6) to get −6r+50r−30-6r + 50r - 30.
  2. Combine Like Terms: Combine like terms on the left side to get 44r−3044r - 30.
  3. Move rr Terms to One Side: Now, combine like terms on the right side, 3r+9+2r3r + 9 + 2r to get 5r+95r + 9.
  4. Simplify Inequality: Next, we'll move all the rr terms to one side by subtracting 5r5r from both sides, so we have 44r−5r−30≤944r - 5r - 30 \leq 9.
  5. Isolate rr Term: Simplify the left side to get 39r−30≤939r - 30 \leq 9.
  6. Isolate r Term: Simplify the left side to get 39r−30≤939r - 30 \leq 9.Then, add 3030 to both sides to isolate the r term, giving us 39r≤3939r \leq 39.
  7. Isolate r Term: Simplify the left side to get 39r−30≤939r - 30 \leq 9.Then, add 3030 to both sides to isolate the r term, giving us 39r≤3939r \leq 39.Finally, divide both sides by 3939 to solve for r, which gives us r≤1r \leq 1.

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