Example Question - solving variable
Here are examples of questions we've helped users solve.
Solving for a Variable with Given Coordinates
To solve for \( n \), we need to use the given information about the coordinates of the points on the line. The coordinates of the two points are given as \( P_1(-18, 18) \) and \( P_2(2, n) \). The slope \( m \) of a line passing through two points \( P_1(x_1, y_1) \) and \( P_2(x_2, y_2) \) can be found using the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Given that the slope is 0 (from the information provided about the equation of the line), this means that the line is horizontal and there is no change in the y-values between points \( P_1 \) and \( P_2 \). Therefore, \( y_1 = y_2 \), or equivalently, \( 18 = n \). So, the value of \( n \) is 18.
Solving an Algebraic Equation for Variable
It appears that you would like to solve the algebraic equation: \[ \frac{2ac + 14}{2a} = 9 \] To solve for c, follow these steps: 1. Multiply both sides of the equation by \(2a\) to get rid of the denominator: \[ 2ac + 14 = 18a \] 2. Subtract 14 from both sides to isolate terms with \(c\) on one side: \[ 2ac = 18a - 14 \] 3. Divide both sides by \(2a\) to solve for \(c\): \[ c = \frac{18a - 14}{2a} \] 4. Simplify the right side if possible: \[ c = 9 - \frac{14}{2a} \] \[ c = 9 - \frac{7}{a} \] So, \(c = 9 - \frac{7}{a}\), assuming \(a \neq 0\).
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