Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = \frac{1}{2} \)
Solution
Sure, let's solve the equation step by step.
**Given Equation:**
\[ 7(3x + 2) - 4 = 5x + 18 \]
**Step 1: Expand the Left Side**
First, distribute the 7 into the terms inside the parentheses:
\[ 7 \times 3x + 7 \times 2 - 4 = 5x + 18 \]
\[ 21x + 14 - 4 = 5x + 18 \]
**Step 2: Simplify the Left Side**
Combine like terms (14 and -4):
\[ 21x + 10 = 5x + 18 \]
**Step 3: Move Variable Terms to One Side**
Subtract \(5x\) from both sides to get all the \(x\) terms on the left:
\[ 21x - 5x + 10 = 18 \]
\[ 16x + 10 = 18 \]
**Step 4: Move Constant Terms to the Other Side**
Subtract 10 from both sides to isolate the term with \(x\):
\[ 16x = 18 - 10 \]
\[ 16x = 8 \]
**Step 5: Solve for \(x\)**
Divide both sides by 16:
\[ x = \frac{8}{16} \]
\[ x = \frac{1}{2} \]
**Solution:**
\[ x = \frac{1}{2} \]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the equation, first, expand the left side: \( 21x + 14 - 4 = 5x + 18 \), which simplifies to \( 21x + 10 = 5x + 18 \). Next, isolate \( x \) by subtracting \( 5x \) from both sides: \( 16x + 10 = 18 \). Then, subtract 10 from both sides: \( 16x = 8 \). Finally, divide by 16, yielding \( x = \frac{1}{2} \). This algebraic manipulation not only highlights the step-by-step journey to find \( x \), but also serves as a great skill for real-world situations – like budgeting, where you can set up equations based on expenses versus income. Solving equations in such contexts can be incredibly useful for personal finance and making informed decisions!
