To solve for [tex]\( x \)[/tex] in the equation [tex]\(\frac{x + a}{b} = 3.5\)[/tex] with the given values [tex]\( a = 22 \)[/tex] and [tex]\( b = 4 \)[/tex], follow these steps:
1. Substitute the given values into the equation:
[tex]\[
\frac{x + 22}{4} = 3.5
\][/tex]
2. Isolate the term containing [tex]\( x \)[/tex] by eliminating the fraction:
Multiply both sides of the equation by 4 to cancel the denominator on the left-hand side:
[tex]\[
4 \times \frac{x + 22}{4} = 3.5 \times 4
\][/tex]
This simplifies to:
[tex]\[
x + 22 = 14
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Subtract 22 from both sides of the equation to isolate [tex]\( x \)[/tex]:
[tex]\[
x + 22 - 22 = 14 - 22
\][/tex]
Simplifying this gives:
[tex]\[
x = -8
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( -8 \)[/tex].
