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Simplify the expression. Write your answers using integers or improper fractions.

3(-3r-r+5)-(1)/(3)r
Answer:

Simplify the expression. Write your answers using integers or improper fractions.\newline3(3rr+5)13r 3(-3 r-r+5)-\frac{1}{3} r \newlineAnswer:

Full solution

Q. Simplify the expression. Write your answers using integers or improper fractions.\newline3(3rr+5)13r 3(-3 r-r+5)-\frac{1}{3} r \newlineAnswer:
  1. Distribute Terms: Distribute the 33 across the terms inside the parentheses.3(3rr+5)=3×3r+3×r+3×53(-3r - r + 5) = 3 \times -3r + 3 \times -r + 3 \times 5=9r3r+15=-9r - 3r + 15
  2. Combine Like Terms: Combine like terms from the result of the distribution.\newline9r3r+15=12r+15-9r - 3r + 15 = -12r + 15
  3. Separate Terms: Write the expression with the term involving rr and the constant term separately.12r+15(13)r-12r + 15 - \left(\frac{1}{3}\right)r
  4. Find Common Denominator: Find a common denominator to combine the terms involving rr. Since the second term involving rr has a denominator of 33, we multiply the first term by 33\frac{3}{3} to get the same denominator. 12r×(33)+15(13)r-12r \times \left(\frac{3}{3}\right) + 15 - \left(\frac{1}{3}\right)r =(363)r(13)r+15\left(-\frac{36}{3}\right)r - \left(\frac{1}{3}\right)r + 15
  5. Combine Terms with rr: Combine the terms involving rr.(363)r(13)r=(361)/3×r\left(-\frac{36}{3}\right)r - \left(\frac{1}{3}\right)r = \left(-36 - 1\right)/3 \times r=(373)r=\left(-\frac{37}{3}\right)r
  6. Combine with Constant Term: Combine the result from Step 55 with the constant term.\newline(373)r+15(-\frac{37}{3})r + 15\newlineSince 1515 does not have a term involving rr, it remains as is.
  7. Final Simplified Expression: Write the final simplified expression.\newlineThe final simplified expression is (373)r+15(-\frac{37}{3})r + 15.

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