Select the correct answer.
What is the solution for $x$ in the equation?
$-2 x+14+10 x=34$
A. $x=\frac{1}{8}$
B. $x=\frac{5}{2}$
C. $x=6$
D. $x=\frac{2}{5}$
Answer (2)
Combine like terms: − 2 x + 10 x + 14 = 34 becomes 8 x + 14 = 34 .
Isolate the x term: Subtract 14 from both sides to get 8 x = 20 .
Solve for x: Divide both sides by 8 to find x = 8 20 .
Simplify: Reduce the fraction to get x = 2 5 .
Explanation
Combine Like Terms First, we need to simplify the given equation by combining like terms. The equation is: − 2 x + 14 + 10 x = 34
Simplify the Equation Combine the terms with x :
( − 2 x + 10 x ) + 14 = 34
8 x + 14 = 34
Isolate the x Term Next, we want to isolate the term with x . To do this, subtract 14 from both sides of the equation: 8 x + 14 − 14 = 34 − 14 8 x = 20
Solve for x Now, to solve for x , divide both sides of the equation by 8: x = 8 20
Simplify the Fraction Simplify the fraction: x = 8 20 = 4 × 2 4 × 5 = 2 5
Final Answer So, the solution for x is 2 5 .
Examples
Imagine you are balancing a budget. You have some income and some expenses. The equation we solved is like figuring out how much you need to save (represented by x) to reach a certain financial goal. By combining your current savings, additional income, and subtracting expenses, you can determine the exact amount you need to save each month to meet your target.
The solution for the equation − 2 x + 14 + 10 x = 34 simplifies to x = 2 5 . Among the provided options, the correct answer is (B).
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