Question
Solve. \[ \frac{7}{8} \mathrm{x}-\frac{1}{4}+\frac{1}{2} \mathrm{x}=\frac{1}{4}+\mathrm{x} \] What is the best first step? A. Divide both șides of the equation by 8 . B. Multiply both sides of the equation by 4 C. Multiply both sides of the equation by 8 . D. Add x on both sides of the equation.
Ask by Newton Garza. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The best first step is to multiply both sides of the equation by 8.
Solution
The equation is:
(7/8)x - 1/4 + (1/2)x = 1/4 + x
It's best to eliminate the fractions first. Notice that the denominators are 8, 4, and 2. The least common multiple of these is 8. Multiplying every term by 8 will clear the fractions and simplify your work. This corresponds to answer choice C.
Thus, the best first step is to multiply both sides of the equation by 8.
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Simplify this solution The Deep Dive
To solve the equation \( \frac{7}{8} x - \frac{1}{4} + \frac{1}{2} x = \frac{1}{4} + x \), the best first step is to eliminate the fractions for easier manipulation. So, you can multiply both sides of the equation by 8 (Option C) to clear the denominators. This will make the equation much simpler to solve! By multiplying by 8, you’ll turn the fractions into whole numbers. This can help avoid common mistakes with fraction arithmetic and keep the solving process straightforward. Once the fractions are cleared, you can collect like terms and solve for \( x \) more easily!
