]]>
]]>
]]>
The official formula is: D = R * T
Distance = Rate x Time
This can also be flipped around to be expressed as R = D / T (Rate = Distance / Time)
Or it can be flipped around yet again to be expressed as T = D / R (Time = Distance / Rate)
This formula is completely liquid and can be "remelded" as needed depending on what you're working on.
]]>
4x - 2x - 5 = 4 + 6x + 3 |
Goal is to isolate x on one side to be able to solve. |
2x - 5 = 7 + 6x |
Combine like terms. |
2x - 5 + 5 = 7 + 6x + 5 |
Add 5 to each side. |
2x = 12 + 6x |
Subtract 6x from each side. |
-4x = 12 |
Then, divide both sides by -4 |
x = -3 |
CHECK your solution by plugging back into the original equation. |
Disclaimer: I did not create nor do I own these videos. I have simply embedded them, courtesy of YouTube. (But I do think this teacher does a fantastic job with his video tutorial series.)
]]>
Here is a list of steps to remember when solving Linear Equations in One Variable.
You may want to become familiar with these steps, each one on its own before putting them all together!
STEP 1: Clear fractions. Get rid of any fractions you see in the original equation by multiplying each side by the least common denominator.
STEP 2: Simplify each side. Use the distributive property to get rid of parentheses and/or combine like terms as necessary.
STEP 3: Isolate the variable terms (often "x") on one side. Use varying properties to get all terms with variables on one side of the equation, with all nubers on the other.
STEP 4: Isolate the variable. Use properties to get an equation with just the variable on one side.
STEP 5: CHECK your solution. Substitute your answer back into the ORIGINAL equation to make sure it is correct.
]]>
2(k - 5) + 3k = k + 6 |
Use the distributive property to simplify and combine like terms. |
2k - 10 + 3k = k + 6 |
Combine like terms. |
5k - 10 = k + 6 |
Then, add 10 to both sides. |
5k = 16 + k |
Then, subtract k from both sides. |
4k = 16 |
Then, divide both sides by 4 |
k = 4 |
CHECK your solution by plugging back into the original equation. |
Disclaimer: I did not create nor do I own these videos. I have simply embedded them, courtesy of YouTube. (But I do think this teacher does a fantastic job with his video tutorial series.)
]]>
For all real numbers A, B and for when C does NOT equal 0, the equations:
A = B and AC = BC are equivalent to one another.
Each side can be multiplied by the same NONZERO number without changing the solution set.
]]>For all real numbers A, B and C, the equations:
A = B and A + C = B + C are equivalent to one another.
The same number may be added to each side of an equation without altering the solution set.
]]>As the name suggests, a linear equation in one variable implies that there is only ONE variable, and that the equation involves only real numbers. A linear equation in one variable can be written in this form: Ax + B = C where A does NOT equal zero.
A linear equation is also a first-degree equation, since the greatest power of any variable is 1.
Here are some examples of linear equations in one variable:
x + 2 = -1
x - 3 = 5
3k + 4 = 10
]]>