Certainly! Let's solve for [tex]\( x \)[/tex] in the given equation step by step.
The given equation is:
[tex]\[
\frac{b + x}{4} = \frac{y + 3}{2}
\][/tex]
Step 1: Eliminate the denominators by multiplying both sides of the equation by 4. This helps to clear the fraction with the denominator 4 on the left side:
[tex]\[
4 \times \left( \frac{b + x}{4} \right) = 4 \times \left( \frac{y + 3}{2} \right)
\][/tex]
Step 2: Simplify both sides. On the left side, the 4 in the numerator and denominator cancel each other out, leaving us with [tex]\( b + x \)[/tex], and on the right side, we multiply [tex]\( \frac{y + 3}{2} \)[/tex] by 4:
[tex]\[
b + x = 4 \times \left( \frac{y + 3}{2} \right)
\][/tex]
Step 3: Further simplify the right side of the equation. Dividing 4 by 2 results in 2:
[tex]\[
b + x = 2 \times (y + 3)
\][/tex]
Step 4: Distribute the 2 on the right side to both terms inside the parentheses:
[tex]\[
b + x = 2y + 6
\][/tex]
Step 5: Isolate [tex]\( x \)[/tex] by subtracting [tex]\( b \)[/tex] from both sides of the equation:
[tex]\[
x = 2y + 6 - b
\][/tex]
So, the solution for [tex]\( x \)[/tex] is:
[tex]\[
x = 2y + 6 - b
\][/tex]
