Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 1 \)
Solution
Sure, let's solve the equation step by step:
\[
2x + 3 = 4(x - 1) + 5
\]
### Step 1: Expand the Right Side
First, distribute the \(4\) on the right side of the equation:
\[
2x + 3 = 4 \cdot x - 4 \cdot 1 + 5
\]
\[
2x + 3 = 4x - 4 + 5
\]
Combine like terms on the right side:
\[
2x + 3 = 4x + 1
\]
### Step 2: Bring Like Terms Together
Subtract \(2x\) from both sides to get all the \(x\)-terms on one side:
\[
2x + 3 - 2x = 4x + 1 - 2x
\]
\[
3 = 2x + 1
\]
Next, subtract \(1\) from both sides to isolate the term with \(x\):
\[
3 - 1 = 2x + 1 - 1
\]
\[
2 = 2x
\]
### Step 3: Solve for \(x\)
Divide both sides by \(2\) to solve for \(x\):
\[
\frac{2}{2} = \frac{2x}{2}
\]
\[
1 = x
\]
### Solution
\[
x = 1
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve the equation \( 2x + 3 = 4(x - 1) + 5 \), first, simplify the right side. Distributing the 4 gives you \( 4x - 4 + 5 \), which simplifies to \( 4x + 1 \). Now the equation looks like \( 2x + 3 = 4x + 1 \). To isolate \( x \), subtract \( 2x \) from both sides, resulting in \( 3 = 2x + 1 \). Next, subtract 1 from both sides, giving \( 2 = 2x \). Finally, divide by 2 to find \( x = 1 \). This type of equation can frequently pop up in real-life scenarios such as budgeting, where you might need to balance expenses and income. Understanding how to manipulate equations like this helps you plan and make informed financial decisions—who knew algebra could save you money, right?
