Questions: Question 11 Use the properties of equality to complete each proof. Given: (2(x+15)=-4(5x-2)); Prove: (x=-1) Statements Reasons 1. [Select] [Select] 2. (2x+30=-20x+8) [Select] 3. (22x+30=8) [Select] 4. [ Select] [Select] 5. [ Select]

Question 11
Use the properties of equality to complete each proof.
Given: (2(x+15)=-4(5x-2)); Prove: (x=-1)

Statements  Reasons

1. [Select]  [Select]

2. (2x+30=-20x+8)  [Select]

3. (22x+30=8)  [Select]

4. [ Select]  [Select]

5. [ Select]
Transcript text: Question 11 Use the properties of equality to complete each proof. Given: $2(x+15)=-4(5 x-2)$; Prove: $x=-1$ \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Statements } & Reasons \\ \hline 1. [Select] & [Select] \\ \hline 2. $2 x+30=-20 x+8$ & [Select] \\ \hline 3. $22 x+30=8$ & [Select] \\ \hline 4. $[$ Select] & [Select] \\ \hline 5. $[$ Select] & \\ \hline \end{tabular}
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Solution

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Solution Steps

To solve the given equation \(2(x+15)=-4(5x-2)\) and prove that \(x=-1\), we will follow these steps:

  1. Distribute the constants on both sides of the equation.
  2. Combine like terms to simplify the equation.
  3. Isolate the variable \(x\) to solve for its value.
Step 1: Distribute the Constants

Distribute the constants on both sides of the equation: \[ 2(x + 15) = -4(5x - 2) \] This becomes: \[ 2x + 30 = -20x + 8 \]

Step 2: Combine Like Terms

Move all terms involving \(x\) to one side and constant terms to the other side: \[ 2x + 20x = 8 - 30 \] Simplifying gives: \[ 22x = -22 \]

Step 3: Solve for \(x\)

Divide both sides by 22 to isolate \(x\): \[ x = \frac{-22}{22} \] Thus, we find: \[ x = -1 \]

Final Answer

The solution to the equation is \(\boxed{x = -1}\).

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