Question
Solve and check the linear equation. \( 3(x-4)+15=2(x+5) \)
Ask by Ruiz Christensen. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 7 \)
Solution
To solve and verify the linear equation:
\[
3(x - 4) + 15 = 2(x + 5)
\]
let's follow these steps:
### Step 1: Expand Both Sides
**Left Side:**
\[
3(x - 4) + 15 = 3x - 12 + 15 = 3x + 3
\]
**Right Side:**
\[
2(x + 5) = 2x + 10
\]
So, the equation becomes:
\[
3x + 3 = 2x + 10
\]
### Step 2: Gather Like Terms
Subtract \(2x\) from both sides to get all \(x\) terms on one side:
\[
3x + 3 - 2x = 2x + 10 - 2x
\]
\[
x + 3 = 10
\]
### Step 3: Isolate \(x\)
Subtract 3 from both sides to solve for \(x\):
\[
x + 3 - 3 = 10 - 3
\]
\[
x = 7
\]
### Solution
\[
x = 7
\]
### Step 4: Check the Solution
Substitute \(x = 7\) back into the original equation to verify:
\[
3(7 - 4) + 15 = 2(7 + 5)
\]
**Calculate Both Sides:**
**Left Side:**
\[
3(3) + 15 = 9 + 15 = 24
\]
**Right Side:**
\[
2(12) = 24
\]
Since both sides equal 24, the solution \(x = 7\) is correct.
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Mind Expander
To solve the equation \( 3(x-4)+15=2(x+5) \), first distribute the constants on both sides: \[ 3x - 12 + 15 = 2x + 10 \] This simplifies to: \[ 3x + 3 = 2x + 10 \] Next, subtract \( 2x \) from both sides: \[ 3x - 2x + 3 = 10 \] This simplifies to: \[ x + 3 = 10 \] Now, subtract 3 from both sides: \[ x = 7 \] To check the solution, substitute \( x = 7 \) back into the original equation: Left side: \[ 3(7-4) + 15 = 3(3) + 15 = 9 + 15 = 24 \] Right side: \[ 2(7+5) = 2(12) = 24 \] Since both sides are equal, the solution is confirmed: \[ x = 7 \]
