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Math  /  Algebra

QuestionQuestion
Solve the following inequality for rr. Write your answer in simplest form. 9r−4(−5r−5)≤−9r+10+59 r-4(-5 r-5) \leq-9 r+10+5
Answer Attempt 1 out of 3 rr □\square Submit Answer

Studdy Solution

STEP 1

1. The inequality 9r−4(−5r−5)≤−9r+10+5 9r - 4(-5r - 5) \leq -9r + 10 + 5 needs to be solved for r r .
2. The solution should be expressed in its simplest form.
3. The inequality involves basic algebraic operations, including distribution and combining like terms.

STEP 2

1. Simplify the inequality by distributing and combining like terms.
2. Isolate the variable r r on one side of the inequality.
3. Solve the inequality for r r .
4. Write the solution in simplest form.

STEP 3

Distribute the −4-4 through the expression −5r−5-5r - 5:
9r−4(−5r−5)≤−9r+10+5 9r - 4(-5r - 5) \leq -9r + 10 + 5
9r+20r+20≤−9r+15 9r + 20r + 20 \leq -9r + 15

STEP 4

Combine like terms on the left side:
(9r+20r)+20≤−9r+15 (9r + 20r) + 20 \leq -9r + 15
29r+20≤−9r+15 29r + 20 \leq -9r + 15

STEP 5

Add 9r 9r to both sides to start isolating r r :
29r+9r+20≤15 29r + 9r + 20 \leq 15
38r+20≤15 38r + 20 \leq 15

STEP 6

Subtract 20 from both sides to further isolate r r :
38r+20−20≤15−20 38r + 20 - 20 \leq 15 - 20
38r≤−5 38r \leq -5

STEP 7

Divide both sides by 38 to solve for r r :
r≤−538 r \leq \frac{-5}{38}

STEP 8

The solution in simplest form is:
r≤−538 r \leq \frac{-5}{38}

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