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For the equation 2(x−5)=9−3x+6+8+3x+7

, the left side of the equation can be simplified using the Distributive Property, and the right side of the equation can be simplified by combining like terms.

3 answers

Let's start simplifying both sides of the given equation step by step:

The equation is: \[ 2(x−5)=9−3x+6+8+3x+7 \]

Step 1: Simplify the left side using the Distributive Property. \[ 2(x−5) = 2 \cdot x - 2 \cdot 5 = 2x - 10 \]

Step 2: Simplify the right side by combining like terms. Let's start with the right side: \[ 9 - 3x + 6 + 8 + 3x + 7 \]

First, combine the constant terms (9, 6, 8, and 7): \[ 9 + 6 + 8 + 7 = 30 \]

Now, combine the terms involving \(x\) (-3x and 3x): \[ -3x + 3x = 0 \]

So, the right side simplifies to: \[ 30 \]

Step 3: Rewrite the equation with the simplified sides.

Now we have: \[ 2x - 10 = 30 \]

Step 4: Solve for \(x\).

Add 10 to both sides: \[ 2x - 10 + 10 = 30 + 10 \] \[ 2x = 40 \]

Now, divide both sides by 2: \[ x = \frac{40}{2} = 20 \]

Final answer: \[ x = 20 \]

Simplify the left side of the equation

Simplify the right side of the equation:

Let's simplify both sides of the equation step by step without skipping any details. The equation is:

\[ 2(x−5) = 9−3x+6+8+3x+7 \]

Simplifying the Left Side

  1. Distribute the 2 across \( (x - 5) \): \[ 2 \cdot x - 2 \cdot 5 = 2x - 10 \]

So, the left side simplifies to: \[ \text{Left side: } 2x - 10 \]

Simplifying the Right Side

  1. Combine like terms on the right side:

    • The constant terms are \( 9 \), \( 6 \), \( 8 \), and \( 7 \).
    • The \( x \) terms are \( -3x \) and \( 3x \).

    First, add the constant terms: \[ 9 + 6 + 8 + 7 = 30 \]

    Now, combine the \( x \) terms: \[ -3x + 3x = 0 \]

Putting it all together, the right side simplifies to: \[ \text{Right side: } 30 \]

Summary of Simplifications

  • Left side: \( 2x - 10 \)
  • Right side: \( 30 \)

Thus, after simplification, the equation can be rewritten as: \[ 2x - 10 = 30 \]