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Chapter 2 Solving Equation - Coggle Diagram
Chapter 2 Solving Equation
L6 Solving Equation with one step
When you see the word "solve" you should find the solution -> the value of x -> true statement (left = right).
A very important concept in solving all equations is to isolate the variable by applying the inverse operation or undo the expressions.
Always check your solution!
Example:
4d + 5 = 20
You want to take out the 5, so you minus 5 on both sides of equal.
4d = 15
Now you want to remove the 4, so you can find the value of d.
d = 15/4
Now you solve 15 divides by 4 and you will get the answer for the value of d.
d = 3.75
After you get the answer for the value of d, you need to double-check if your solution is right.
When you want to check your solution, you need to use inverse operation which you undo the expressions.
4(3.75) + 5 = 20
You will need to solve both sides of the equal sign to check if your solution is correct.
20 = 20
If the answer is the same for both sides and the same as the question's answer then your answer and solution are correct.
Solving with Multiple steps
The solution of a multi-step equation can be found using the properties of equality and real numbers and inverse operations to form a series of simpler expression.
The ultimate goal is to isolate the variables.
Identity is an equation with many solutions.
No-solution equation is an equation that has no solution.
Solving proportion
Proportion is an equation that always contain an equal sign and two fraction (ratio).
We can solve proportion by using ratio, cross product properties, and inverse operation.
Cross product properties is useful in solving proportions because it is faster than using the other solving problem.
Properties and similar figures
Similar figures is figures that have the same shape but not necessarily the same size. The corresponding angles are the same.
Scale drawing is a drawing that is similar to an actual object or place.
Scale model is a three-dimensional model that is similar to a three-dimensional object.he ratio of a linear measurement of a model to the corresponding linear measurement of the actual object is always the same.
You will need to find missing lengths in similar figures and use similar figures when measuring indirectly when you are solve or find the properties of similar figures.
This picture down here shows is the example of the changing the length of the model to actual length.
Literal Equations & Formula
Literal equation is an equation that involves two or more variables. Formula is a mathematical relationship or a rule expressed in symbols.
Example of literal equation: x + y = 5, a = 1/2
Example of formula: c = πd, p = 2l + 2w
Example 1:
a = 0.29, n = 300
a = h/n
0.29 = h/300
h = a
n
0.29
300 = h
87 = h
Ratio, Rates and conversions
A conversion factor is a ratio of two equivalent measures in different units.
A ratio compares two numbers by division. And it can be written as: a/b, a to b, and a : b.
A rate is a ratio that compares two quantities in different units. A rate with a denominator of 1 unit is unite rate.
Percent
Percent of base is part.
percent error = estimated value - actual/ actual value
GPD = Greatest possible value
