Question

find the value of x in the equation: 1/4x + 1/2 = 3/8

Explanation:

Step1: Subtract 1/2 from both sides

We start with the equation $\frac{1}{4}x + \frac{1}{2} = \frac{3}{8}$. To isolate the term with $x$, we subtract $\frac{1}{2}$ from both sides. First, we need to find a common denominator for $\frac{1}{2}$ and $\frac{3}{8}$, which is 8. So $\frac{1}{2}=\frac{4}{8}$. Then the equation becomes $\frac{1}{4}x+\frac{4}{8}=\frac{3}{8}$. Subtracting $\frac{4}{8}$ from both sides gives $\frac{1}{4}x=\frac{3}{8}-\frac{4}{8}$.
$\frac{1}{4}x=\frac{3 - 4}{8}=-\frac{1}{8}$

Step2: Multiply both sides by 4

To solve for $x$, we multiply both sides of the equation $\frac{1}{4}x = -\frac{1}{8}$ by 4. This will cancel out the coefficient of $x$ on the left side. So $x = -\frac{1}{8}\times4$.
$x = -\frac{4}{8}=-\frac{1}{2}$ (Wait, but let's check again. Wait, maybe I made a mistake in the first step. Wait, let's re - do the first step. The original equation is $\frac{1}{4}x+\frac{1}{2}=\frac{3}{8}$. Subtract $\frac{1}{2}$ from both sides: $\frac{1}{4}x=\frac{3}{8}-\frac{1}{2}$. Convert $\frac{1}{2}$ to eighths: $\frac{1}{2}=\frac{4}{8}$. So $\frac{3}{8}-\frac{4}{8}=-\frac{1}{8}$. Then multiply both sides by 4: $x = -\frac{1}{8}\times4=-\frac{1}{2}$. But looking at the options, one of the options is - 1/2? Wait, the visible options are 2/3, - 1/4, 1/2, and then a partial - 1/... Wait, maybe I misread the equation. Wait, maybe the equation is $\frac{1}{4}x+\frac{1}{2}=\frac{3}{8}$? Wait, no, maybe it's $\frac{1}{4}x+\frac{1}{2}=\frac{3}{8}$? Wait, let's check the calculation again.

Wait, let's start over. Equation: $\frac{1}{4}x+\frac{1}{2}=\frac{3}{8}$

Step 1: Subtract $\frac{1}{2}$ from both sides.
$\frac{1}{4}x=\frac{3}{8}-\frac{1}{2}$
Find a common denominator for $\frac{1}{2}$ and $\frac{3}{8}$, which is 8. So $\frac{1}{2}=\frac{4}{8}$.
$\frac{1}{4}x=\frac{3}{8}-\frac{4}{8}=\frac{3 - 4}{8}=-\frac{1}{8}$

Step 2: Multiply both sides by 4 to solve for $x$.
$x = -\frac{1}{8}\times4=-\frac{4}{8}=-\frac{1}{2}$

Wait, but in the options, there is a - 1/2 (partially visible). But among the given visible options, - 1/4, 1/2, 2/3, and - 1/... So maybe the correct answer is - 1/2, but let's check the calculation again.

Wait, maybe the equation was written wrong. Wait, maybe it's $\frac{1}{4}x+\frac{1}{2}=\frac{3}{8}$? Or maybe $\frac{1}{4}x+\frac{1}{2}=\frac{3}{8}$? Wait, no, let's check with the answer options. The options are 2/3, - 1/4, 1/2, and - 1/2 (partially). So according to our calculation, $x = -\frac{1}{2}$. But let's check the steps again.

Wait, another way: Let's plug in the options. Let's try $x=-1/4$. Then $\frac{1}{4}\times(-\frac{1}{4})+\frac{1}{2}=-\frac{1}{16}+\frac{8}{16}=\frac{7}{16}
eq\frac{3}{8}$. Try $x = 1/2$: $\frac{1}{4}\times\frac{1}{2}+\frac{1}{2}=\frac{1}{8}+\frac{4}{8}=\frac{5}{8}
eq\frac{3}{8}$. Try $x = 2/3$: $\frac{1}{4}\times\frac{2}{3}+\frac{1}{2}=\frac{1}{6}+\frac{3}{6}=\frac{4}{6}=\frac{2}{3}
eq\frac{3}{8}$. Try $x=-1/2$: $\frac{1}{4}\times(-\frac{1}{2})+\frac{1}{2}=-\frac{1}{8}+\frac{4}{8}=\frac{3}{8}$, which matches the right - hand side. So the correct value of $x$ is $-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$ (Assuming the fourth option is - 1/2)