1. Solving for a Specific Variable
(Literal Equations)
Algebra Glencoe McGraw-Hill JoAnn Evans

2. contains more than one variable.
Literal Equations
A literal equation is an equation that
contains more than one variable.
A literal equation can be solved for one of its “letters” (variables) by using inverse operations to isolate that variable on one side of the equal sign.
The word "literal" comes from the Latin word for "letter".

3. Solve the equation for both x and y:
Solve for x:
Solve for y:
4x + y = 7
4x + y = 7
-y y
-4x x
4x = -y + 7
y = – 4x + 7 1
4x = -y +7
x = -y + 7 4
In each case above, one of the variables was isolated using the same inverse operations we do when solving equations.

4. Solve the equation for the indicated variable:
Solve for x:
Solve for y:
5x + 2y = 8
-2y y 1
5x = –2y + 8 1
5x = –2y + 8
x = –2y + 8 5

5. Multiply by the reciprocal to clear the fraction.
Solve the triangle area formula for b: 1
Multiply by the reciprocal to clear the fraction. 1
Divide both sides by h to isolate the b.

6. Solve for d:
Notice that there are two “d” variables, one on each side of the equation.
Use inverse operations to get both “d”s on the same side of the equation. 1

7. Solve for b:
Solve for a: 1 1 1

8. Solve for k: 1

9. The variable x is being multiplied by the quantity 1 + y.
Solve for x:
The variable x is being multiplied by the quantity 1 + y.
Divide each side of the equation by that quantity to isolate the x. 1
In the final answer, put the variable term first.

10. The variable h is being multiplied by the quantity a + b.
Solve for h:
Clear the fraction. 1
The variable h is being multiplied by the quantity a + b.
Divide each side of the equation by that quantity to isolate the h. 1