Question

Determine the value of the variable in the simplified expressions.

What is the value of x?

gx+h−3=1g6+1h3
x=


What is the value of y?

b4c−7=byc7
y=

Answer 1

To determine the values of \( x \) and \( y \) in the simplified expressions you provided, we will solve each equation step-by-step.

### 1. Solve for \( x \):

You provided the equation:
\[
gx + h - 3 = 1g6 + 1h3
\]

Assuming \( 1g6 \) represents \( g \cdot 6 \) and \( 1h3 \) represents \( h \cdot 3 \), the equation can be rewritten as:
\[
gx + h - 3 = 6g + 3h
\]

Next, to isolate the term involving \( x \), we subtract \( h \) from both sides:
\[
gx - 3 = 6g + 3h - h
\]
\[
gx - 3 = 6g + 2h
\]

Now, we add \( 3 \) to both sides:
\[
gx = 6g + 2h + 3
\]

Finally, divide both sides by \( g \):
\[
x = \frac{6g + 2h + 3}{g}
\]

Thus:
\[
x = 6 + \frac{2h}{g} + \frac{3}{g}
\]

### 2. Solve for \( y \):

You provided the equation:
\[
b4c - 7 = byc7
\]

Assuming \( b4c \) represents \( b \cdot 4 \cdot c \) and \( byc7 \) represents \( b \cdot y \cdot c \cdot 7 \):
\[
b \cdot 4 \cdot c - 7 = b \cdot y \cdot c \cdot 7
\]

To isolate \( y \), we first add \( 7 \) to both sides:
\[
b \cdot 4 \cdot c = b \cdot y \cdot c \cdot 7 + 7
\]

Now, we can factor out \( b \cdot c \) from the left side:
\[
4bc = 7byc + 7
\]

Next, we can factor out \( b \) from the right-side:
\[
4bc = byc \cdot 7 + 7
\]

To isolate \( y \), we can move \( 7ybc \) to the other side:
\[
4bc - 7 = 7byc
\]

Now, divide through by \( 7bc \):
\[
y = \frac{4c - 7}{7c}
\]

So, the solution for \( y \) can be simplified further if needed:
\[
y = \frac{4}{7} - \frac{1}{b}
\]

### Conclusion:
- The value of \( x = 6 + \frac{2h}{g} + \frac{3}{g} \)
- The value of \( y = \frac{4c - 7}{7c} \)

Please verify if my interpretation of the variable expressions is correct, and if any specific variables or relationships were intended but not explicitly stated, feel free to clarify!