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If the solution to the equation 0.8(15-3x)=2x-15.3-ax is x=6.5, what is the value of a ?

If the solution to the equation 0.8(15−3x)=2x−15.3−ax 0.8(15-3 x)=2 x-15.3-a x is x=6.5 x=6.5 , what is the value of a a ?

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Full solution

Q. If the solution to the equation 0.8(15−3x)=2x−15.3−ax 0.8(15-3 x)=2 x-15.3-a x is x=6.5 x=6.5 , what is the value of a a ?
  1. Plug and Simplify: First, let's plug x=6.5x=6.5 into the equation and simplify the left side: 0.8(15−3(6.5))=0.8(15−19.5)=0.8(−4.5)0.8(15 - 3(6.5)) = 0.8(15 - 19.5) = 0.8(-4.5).
  2. Calculate Left Side: Now, let's calculate the left side: 0.8×−4.5=−3.60.8 \times -4.5 = -3.6.
  3. Plug into Right Side: Next, we plug x=6.5x=6.5 into the right side of the equation:\newline2(6.5)−15.3−a(6.5)2(6.5) - 15.3 - a(6.5).
  4. Simplify Right Side: Let's simplify the right side:\newline13−15.3−6.5a=−2.3−6.5a13 - 15.3 - 6.5a = -2.3 - 6.5a.
  5. Equation from Both Sides: Now we have the equation from both sides:\newline−3.6=−2.3−6.5a-3.6 = -2.3 - 6.5a.
  6. Solve for a: Let's solve for a by adding 2.32.3 to both sides:\newline−3.6+2.3=−6.5a-3.6 + 2.3 = -6.5a.
  7. Simplify Left Side: Now we simplify the left side:\newline−1.3=−6.5a-1.3 = -6.5a.
  8. Divide to Solve aa: Finally, we divide both sides by −6.5-6.5 to solve for aa:a=−1.3−6.5.a = \frac{-1.3}{-6.5}.
  9. Final Result: After the division, we get: a=0.2a = 0.2.

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