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Solve for qq.\newline3(q−14)+3=183(q - 14) + 3 = 18\newlineq=q = _____

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Full solution

Q. Solve for qq.\newline3(q−14)+3=183(q - 14) + 3 = 18\newlineq=q = _____
  1. Distribute 33 into parentheses: Distribute the 33 into the parentheses.\newlineWe need to apply the distributive property to the expression 3(q−14)3(q - 14). This means we multiply 33 by both qq and −14-14.\newline3×q=3q3 \times q = 3q\newline3×(−14)=−423 \times (-14) = -42\newlineSo, 3(q−14)3(q − 14) becomes 3q−423q - 42.
  2. Write new equation after distribution: Write the new equation after distribution.\newlineAfter distributing, our equation is now 3q−42+3=183q - 42 + 3 = 18.
  3. Combine like terms: Combine like terms on the left side of the equation.\newlineWe have −42-42 and +3+3 on the left side, which are like terms. We combine them to simplify the equation.\newline−42+3=−39-42 + 3 = -39\newlineSo, the equation now is 3q−39=183q - 39 = 18.
  4. Add 3939 to isolate term: Add 3939 to both sides of the equation to isolate the term with qq. To get 3q3q by itself on one side, we need to get rid of −39-39. We do this by adding 3939 to both sides of the equation. 3q−39+39=18+393q - 39 + 39 = 18 + 39 This simplifies to 3q=573q = 57.
  5. Divide both sides to solve: Divide both sides of the equation by 33 to solve for qq. To find the value of qq, we divide both sides of the equation by 33. 3q3=573\frac{3q}{3} = \frac{57}{3} This simplifies to q=19q = 19.

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