Solve for y:
$22 = 6y + 7$
$22 = 6y + 7$
Solve for y:
$22 = 6y + 7$
The given equation is \(22 = 6y + 7\), where \(y\) is the variable we need to solve for. This is a linear equation in one variable, representing a relationship where a constant value (22) is set equal to a linear expression involving \(y\). Our goal is to isolate \(y\) by performing algebraic operations on both sides of the equation.
To begin isolating the variable \(y\), we first subtract the constant term \(7\) from both sides of the equation:
\[22 - 7 = 6y + 7 - 7\]
Simplifying both sides, we get:
\[15 = 6y\]
This reduces the equation to a simpler form where the variable \(y\) is multiplied by a coefficient.
Now, we isolate \(y\) by dividing both sides of the equation by the coefficient \(6\):
\[\frac{15}{6} = \frac{6y}{6}\]
Simplifying the fractions, we have:
\[y = \frac{15}{6}\]
By dividing both the numerator and the denominator by their greatest common divisor, which is 3, we simplify the fraction:
\[y = \frac{15 \div 3}{6 \div 3} = \frac{5}{2}\]
Thus, the value of \(y\) is \(\frac{5}{2}\), or \(2.5\).
Linear equations like this are fundamental in everyday scenarios. For example, if a taxi charges a flat fee of \(\$7\) plus \(\$6\) per kilometer, and you paid \(\$22\) for a ride, you can set up the equation \(6y + 7 = 22\) to determine the distance \(y\) you traveled. Solving this equation helps you verify your travel distance based on the total cost.