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Solve for a. Give an exact answer. {:[3+0.5(4a+8)=9-2a],[a=◻]:}

Solve for a a .\newlineGive an exact answer.\newline3+0.5(4a+8)=9−2aa=□ \begin{array}{l} 3+0.5(4 a+8)=9-2 a \\ a=\square \end{array}

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Full solution

Q. Solve for a a .\newlineGive an exact answer.\newline3+0.5(4a+8)=9−2aa=□ \begin{array}{l} 3+0.5(4 a+8)=9-2 a \\ a=\square \end{array}
  1. Distribute 0.50.5 into (4a+8)(4a + 8): Simplify the equation by distributing 0.50.5 into (4a+8)(4a + 8).\newline0.5(4a)+0.5(8)=2a+40.5(4a) + 0.5(8) = 2a + 4\newlineNow the equation is 3+2a+4=9−2a3 + 2a + 4 = 9 - 2a
  2. Combine like terms on the left side: Combine like terms on the left side of the equation.3+4=73 + 4 = 7, so now we have 7+2a=9−2a7 + 2a = 9 - 2a
  3. Add 2a2a to both sides: Add 2a2a to both sides of the equation to get all the aa terms on one side.\newline7+2a+2a=9−2a+2a7 + 2a + 2a = 9 - 2a + 2a\newlineThis simplifies to 7+4a=97 + 4a = 9
  4. Isolate the term with aa: Subtract 77 from both sides of the equation to isolate the term with aa.
    7+4a−7=9−77 + 4a - 7 = 9 - 7
    This simplifies to 4a=24a = 2
  5. Solve for a: Divide both sides of the equation by 44 to solve for a.\newline4a4=24\frac{4a}{4} = \frac{2}{4}\newlineThis simplifies to a=0.5a = 0.5

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