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Solve the following equation for x. Express your answer in the simplest form. -2(3x+8)=-28 x-35

Solve the following equation for x x . Express your answer in the simplest form.\newline−2(3x+8)=−28x−35 -2(3 x+8)=-28 x-35 \newline

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Full solution

Q. Solve the following equation for x x . Express your answer in the simplest form.\newline−2(3x+8)=−28x−35 -2(3 x+8)=-28 x-35 \newline
  1. Distribute −2-2: First, let's distribute the −2-2 on the left side of the equation to both 3x3x and 88.
    −2×3x=−6x-2 \times 3x = -6x
    −2×8=−16-2 \times 8 = -16
    So the equation becomes:
    −6x−16=−28x−35-6x - 16 = -28x - 35
  2. Combine Like Terms: Next, we want to get all the xx terms on one side and the constants on the other side. Let's add 28x28x to both sides of the equation to move the xx terms to the left side.\newline−6x+28x−16=−28x+28x−35-6x + 28x - 16 = -28x + 28x - 35\newlineThis simplifies to:\newline22x−16=−3522x - 16 = -35
  3. Isolate x Term: Now, let's add 1616 to both sides to isolate the xx term.\newline22x−16+16=−35+1622x - 16 + 16 = -35 + 16\newlineThis simplifies to:\newline22x=−1922x = -19
  4. Solve for x: Finally, we divide both sides by 2222 to solve for xx.\newline22x22=−1922\frac{22x}{22} = \frac{-19}{22}\newlineThis simplifies to:\newlinex=−1922x = \frac{-19}{22}

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