An equation with more than one variable is sometimes called a formula. Formulas show us how the variables are related to one another (e.g. A = LW). This section explains how you can rearrange formulas to isolate for a given variable.
Click on the titles below to view each example.
Rearrange A equals 2 times l plus 2 times w to isolate for w.
Line 1: We want to get w all by itself on one side of the equation, so we first we have to undo plus 2l by subtracting 2l from both sides, so the equation is A minus 2l equals 2l minus 2l plus 2w.
Line 2: Simplify the equation to A minus 2l equals 2w.
Line 3: To undo the multiplication we divide both sides by 2 so the equation becomes A minus 2l all over 2 equals 2w over 2.
Line 4: Simplify to get A minus 2l all over 2 equals w.
Line 5: Therefore, the equation rearranged for w is w equals A minus 2l all over 2.
Solve for r in the equation A equals P times open bracket 1 plus r t close bracket.
Line 1: We want to get r all by itself on one side of the equation, so first we must remove the brackets by multiplying each term inside the brackets by P. The equation becomes A equals P plus P r t.
Line 2: Remove P on the right side of the equation by subtracting P from both sides so the equation becomes A minus P equals P minus P plus P r t.
Line 3: Simplify the equation to A minus P equals P r t.
Line 4: To isolate for r, we need to undo the multiplication, so we divide both sides by P t, so the equation becomes A minus P all over P t equals P r t over P t.
Line 5: Simplify to get A minus P all over P t equals r
Line 5: Therefore, the equation solved for r is r equals A minus P all over P t.
Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window