Literal Equations

Example 1 Formula relating distance, rate and time.. Identify what you want to get by itself! Since there is an r right next to the t, it means multiplication. To get rid of it then, we must divide by r. The r’s cancel out Now t is by itself and we are done! If we knew the rate and the distance, could we solve to find the time of a trip?

Example 2 Formula for area of a triangle. Get rid of the fraction by multiplying by what is on the bottom. Identify what you want to get by itself! The 2’s cancel out Since there is a b right next to the h, it means multiplication. To get rid of it then, we must divide by b. The b’s cancel out Now h is by itself and we are done! If we knew the base and the area of a triangle, you can solve for the height and know what it is.

Example 3 Formula for area of a trapezoid. Get rid of the fraction by multiplying by what is on the bottom. Identify what you want to get by itself! The 2’s cancel out Now, what we want is inside the parenthesis, so just get rid of the h right away. There’s no symbol, so it must be multiplication. To get rid of it, divide! The h’s cancel out Now b2 is by itself and we are done! If we knew a base, the height and the area of a trapezoid, you can solve for the other base and know what it is. There is still a b1 by the b2, so we need to get rid of it. Subtract it off.

Example 4 Formula for area of a trapezoid. Get rid of the fraction by multiplying by what is on the bottom. Identify what you want to get by itself! The 2’s cancel out Now, what we want is outside the parenthesis, so let’s get rid of the parentheses. There’s no symbol, so it must be multiplication. To get rid of it, divide! Remember to divide by ALL the junk in the parentheses! Now h is by itself and we are done! If we knew the bases and the area of a trapezoid, you can solve for the other base and know what it is.

Example 5 The furthest thing from the y is the 3x. So we get rid of the whole thing by subtracting 3x from both sides. Identify what you want to get by itself! The 3x’s cancel out We need to get y by itself, but there’s a fraction there! To get rid of it, flip and multiply. Now the 2s and 3s will cancel on the left side Now y is by itself and we are done! Now for a little bit harder, lets look at some fractions. Solve for y.

Example 6 The furthest thing from the y is the c. It’s also the ugliest thing there, because it’s on the bottom of a fraction. So to get rid of it, multiply by c. Identify what you want to get by itself! The c’s cancel out We need to get y by itself, but there’s a 2 there! Between the 2 and the y, there is a + sign. To get rid of it, subtract. Now the 2s will cancel on the left side Now y is by itself and we are done! Now for a little bit harder, lets look at some fractions. Solve for y.

Example 7 Uh-oh! There’s two x’s! That’s confusing. Let’s make it just one. Factor out the x, and see what remains. Identify what you want to get by itself! When we factor out: look at what is in common. Put that outside parentheses and leave the rest inside them. We need to get x by itself, but there’s junk in parentheses there! To get rid of it, divide by the junk. Now the parentheses will cancel on the right side Now x is by itself and we are done! Now for a little bit harder, lets factor. Solve for x.

Example 8 Uh-oh! There’s two v’s! That’s confusing. Let’s make it just one. Factor out the v, and see what remains. Identify what you want to get by itself! When we factor out: look at what is in common. Put that outside parentheses and leave the rest inside them. We need to get v by itself, but there’s junk in parentheses there! To get rid of it, divide by the junk. Now the parentheses will cancel on the right side Now v is by itself and we are done! Again, lets factor. Solve for v.

Example 9 Uh-oh! There’s two v’s! That’s confusing. Let’s make it just one. Factor out the v, and see what remains. Identify what you want to get by itself! When we factor out: look at what is in common. Put that outside parentheses and leave the rest inside them. We need to get v by itself, but there’s junk in parentheses there! To get rid of it, divide by the junk. Now the parentheses will cancel on the right side Now v is by itself and we are done! Again, lets factor. Solve for v.

Example 10 Uh-oh! There’s two v’s! That’s confusing. Let’s make it just one. Factor out the v, and see what remains. Identify what you want to get by itself! When we factor out: look at what is in common. Put that outside parentheses and leave the rest inside them. We need to get v by itself, but there’s junk in parentheses there! To get rid of it, divide by the junk. Now the parentheses will cancel on the right side Now v is by itself and we are done! Again, lets factor. Solve for w.

Example 11 Now you try. Solve for y.

Harder still! Just take it step by step, and remember that the variables are just variables, whether they have a 0 on the bottom, or a k on the bottom or what! Solve for a:

Harder still! Just take it step by step, and remember that the variables are just variables, whether they have a 0 on the bottom, or a k on the bottom or what! Solve for r:

Harder still! Just take it step by step, and remember that the variables are just variables, whether they have a 0 on the bottom, or a k on the bottom or what! Solve for L:

Harder still! Just take it step by step, and remember that the variables are just variables, whether they have a 0 on the bottom, or a k on the bottom or what! Solve for q 1 :

Harder still! Just take it step by step, and remember that the variables are just variables, whether they have a 0 on the bottom, or a k on the bottom or what! Solve for g  :