solve this ---**Question Stem:**
If $\frac{1}{2} + 4x = -x + 2$, what is the value of $x$?
**Other Relevant Text:**
Choose 1 answer:
**Options:**
A. $x = \frac{3}{10}$
B. $x = \frac{1}{2}$
C. $x = \frac{5}{6}$
D. $x = \frac{15}{2}$
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We need to solve the linear equation one half plus four x equals negative x plus two. Let's visualize this by graphing both sides of the equation. The left side is one half plus four x, shown in blue. The right side is negative x plus two, shown in red. The solution is where these two lines intersect.
Now let's solve this equation step by step. First, we need to collect all the x terms on one side. We'll add x to both sides of the equation. On the left side, we have one half plus four x plus x, which gives us one half plus five x. On the right side, we have negative x plus two plus x, which simplifies to just two.
Next, we need to isolate the x term. We subtract one half from both sides. On the right side, we calculate two minus one half. Converting two to a fraction gives us four halves minus one half, which equals three halves. So now we have five x equals three halves.
Finally, we solve for x by dividing both sides by 5. We have x equals three halves divided by 5. This is the same as three halves times one fifth. Multiplying the fractions gives us three times one over two times five, which equals three tenths. Therefore, x equals three tenths, which corresponds to answer choice A.
To summarize our solution: We started with the equation one half plus four x equals negative x plus two. We added x to both sides to collect all x terms on the left. Then we subtracted one half from both sides to isolate the term with x. Finally, we divided by five to get x equals three tenths. The correct answer is choice A.