140 Chapter 2 Linear Equations and Inequalities in One Variable already solved for F. But when the Fahrenheit temperature was given, we had to solve the equation for C to find the equivalent Celsius value. An alternate way of dealing with this is to first rewrite the Fahrenheit formula so that the variable C is isolated on one side of the equation. Then we can substitute the known Fahrenheit value. When working with formulas and algebraic equations containing more than one variable, it is sometimes necessary for us to rewrite the formula or equation so that a different variable is isolated. ���������������������� Solving a Formula for a Specified Variable Step 1: Multiply both sides of the equation by the LCD to clear fractions from the equation, if necessary. Step 2: Apply the distributive property to clear parentheses as needed. Step 3: Apply the addition property of equality to move all terms containing the specified variable to one side of the equation and all other terms to the other side of the equation. Step 4: Apply the multiplication property of equality to obtain a coefficient of 1 on the specified variable. �� ������������������������ ������������������ Solve each formula for the specified variable. 3a. The formula A = lw is used to find the area of a rectangle. Solve for w. 3b. The formula P = 2l + 2w gives the perimeter of a rectangle. Solve for l. 3c. The formula F = 9 5 C + 32 converts degrees Celsius to degrees Fahrenheit. Solve for C. 3d. Solve 3x - y = 6 for y. 3e. Solve 2x + 3y = 12 for y. Solutions 3a. A = lw A l = lw l A l = w So, w = A l . 3b. P = 2l + 2w P - 2w = 2l + 2w - 2w P - 2w = 2l P - 2w 2 = 2l 2 P - 2w 2 = l So, l = P - 2w 2 . ������������ P - 2w 2 = P 2 - 2w 2 = P 2 Highlight the variable to isolate. Divide each side by l. Simplify. Highlight the variable to isolate. Subtract 2w from each side. Simplify. Divide each side by 2. Simplify. - w. It is not equal to P - w.
hendricks_beginning_algebra_1e_ch1_3
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