Question
9. \( 3(2x-5)+2(4x+7)=5(3x+1) \)
Ask by Washington Parsons. in Indonesia
Jan 20,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -6 \)
Solution
Let's solve the equation step by step:
\[
3(2x - 5) + 2(4x + 7) = 5(3x + 1)
\]
### Step 1: Expand the Parentheses
Multiply each term inside the parentheses by the factor outside:
\[
3 \cdot 2x + 3 \cdot (-5) + 2 \cdot 4x + 2 \cdot 7 = 5 \cdot 3x + 5 \cdot 1
\]
This simplifies to:
\[
6x - 15 + 8x + 14 = 15x + 5
\]
### Step 2: Combine Like Terms
Combine the \(x\) terms and the constant terms on the left side:
\[
(6x + 8x) + (-15 + 14) = 15x + 5
\]
\[
14x - 1 = 15x + 5
\]
### Step 3: Get All \(x\) Terms on One Side
Subtract \(14x\) from both sides to get the \(x\) terms on one side:
\[
14x - 1 - 14x = 15x + 5 - 14x
\]
\[
-1 = x + 5
\]
### Step 4: Isolate \(x\)
Subtract 5 from both sides to solve for \(x\):
\[
-1 - 5 = x
\]
\[
-6 = x
\]
### Conclusion
The solution to the equation is:
\[
x = -6
\]
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Simplify this solution Bonus Knowledge
To solve the equation \( 3(2x-5)+2(4x+7)=5(3x+1) \), let's start by distributing the terms. First, distribute on the left side: \( 3(2x) - 3(5) + 2(4x) + 2(7) \) This simplifies to: \( 6x - 15 + 8x + 14 \) Now, combine like terms: \( (6x + 8x) + (-15 + 14) = 14x - 1 \) Now, distribute on the right side: \( 5(3x) + 5(1) \) This simplifies to: \( 15x + 5 \) We now have: \( 14x - 1 = 15x + 5 \) Next, move the \( 15x \) to the left side: \( 14x - 15x - 1 = 5 \) This simplifies to: \( -x - 1 = 5 \) Now, add 1 to both sides: \( -x = 5 + 1 \) \( -x = 6 \) Finally, multiply both sides by -1 to solve for \( x \): \( x = -6 \) So, the solution to the equation is \( x = -6 \).
