If you're asked to solve the following equation for b: ( ax + b ) = c, the first step is to isolate the variable by adding ( -a ) to both sides of the equation. ax + ( - ax ) + b = c + ( - ax ). This yields a solution: b = c - ax . You can still confirm the accuracy of your answer by plugging the value of b into the original equation: ax + ( c - ax ) = c, as you would with a linear equation.
Literal equations containing fractions are also dealt with as in a linear equation. Solve for g: ( g / 3 + x ) = ( 2x + 7 ). First isolate g by adding ( -x ) to both sides: g / 3 + x + ( - x) = 2x + ( -x ) + 7, resulting in: g / 3 = x + 7. Now multiply both sides by 3 for the solution: ( g / 3 ) x ( 3 ) = ( x + 7 ) x ( 3 ), yielding: g = 3x + 21.
Suppose you're given the perimeter of a rectangle and the length, and must find the width. Setting out the formula for the perimeter and solving for w gives you the format for solving this problem: P = 2l + 2w. Add ( - 2l) to both sides: P + ( - 2l ) = 2w + 2l + ( - 2l ). This results in: 2w = P - 2l. Then multiply both sides by (1 / 2): (1 / 2)( 2w ) = (1 / 2)( P - 2l ), yielding a solution of w = ( P / 2 ) - l. If you're given values: P = 24 and l = 7, plugging in those values yields the value of w: w = (( 24 / 2 ) - 7 )= ( 12 - 7 ) = 5
If Rachel speed-walks 10 miles and it takes her 3 hours to do it, how many miles per hour can she speed-walk? Here the solution is for her rate of speed. The distance formula D = rt can be manipulated to solve for r (or rate) by multiplying both sides by (1 / t ): D ( 1 / t ) = r t ( 1 / t ), yielding the solution: r = D / t. If you plug in the values D = 10 and t = 3, the answer for r = 10 / 3 or 3 1 / 3 miles per hour.