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Solve the following equation for x. Express your answer in the simplest form. -8(5x-3)=-5x+5

Solve the following equation for x x . Express your answer in the simplest form.\newline−8(5x−3)=−5x+5 -8(5 x-3)=-5 x+5 \newline

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Full solution

Q. Solve the following equation for x x . Express your answer in the simplest form.\newline−8(5x−3)=−5x+5 -8(5 x-3)=-5 x+5 \newline
  1. Apply Distributive Property: Apply the distributive property to the left side of the equation to eliminate the parentheses.\newline−8(5x−3)=−8×5x+−8×−3-8(5x-3) = -8 \times 5x + -8 \times -3
  2. Simplify Multiplication: Simplify the multiplication on the left side of the equation.−40x+24=−5x+5-40x + 24 = -5x + 5
  3. Add Like Terms: Add 40x40x to both sides of the equation to move the xx terms to one side.\newline−40x+40x+24=−5x+40x+5-40x + 40x + 24 = -5x + 40x + 5
  4. Combine Like Terms: Simplify the equation by combining like terms. 24=35x+524 = 35x + 5
  5. Subtract Constant: Subtract 55 from both sides of the equation to isolate the term with xx.\newline24−5=35x+5−524 - 5 = 35x + 5 - 5
  6. Isolate xx Term: Simplify the subtraction on both sides of the equation.19=35x19 = 35x
  7. Divide by 3535: Divide both sides of the equation by 3535 to solve for xx.1935=35x35\frac{19}{35} = \frac{35x}{35}
  8. Simplify Division: Simplify the division to find the value of xx.x=1935x = \frac{19}{35}

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