Solving Formulas

Solving Formulas A formula is an algebraic sentence with more than one variable. Since a formula has more than one variable, we must be told which variable to solve for (isolate).

Solving Formulas When we isolate one variable in a formula, we need to move other variables and numbers to the other side of the equation. To move a variable that is added to the expression, add the opposite variable to both sides. To move a variable that is multiplied or divided by the expression, multiply the reciprocal on both sides.

Variable b is now isolated. Examples To isolate b , we must move the variable a . Variable a is multiplied by variable b , so multiply both sides by the reciprocal of a . Or divide both sides by a. (Same result) Multiply both sides by . Or divide both side by a. Variable b is now isolated.

Examples To isolate y , we must move the term 3x away from y to the other side of the equation .The term 3x is added to variable y , so add -3x to both sides. ( Or just subtract 3x. Remember that adding a negative is the same as subtracting.) Subtract 3x to both sides. Warning: 9 and -3x are NOT like terms! Variable y is now isolated.

Subtract 4b to both sides. Warning: c and -4b are NOT like terms! Examples To isolate a , we must move the term 4b and the coefficient, 2, away from a . Solving equations means we still need to reverse the order of operations, so take care of adding/subtracting first. Subtract 4b to both sides. Warning: c and -4b are NOT like terms! 2 2 Divide by 2 on both sides. SO

Solve each formula for the stated variable. Try These! Solve each formula for the stated variable.