where is the mistake
a = a Reflexive property
a = b then b = a Symmetric property
a = b and b = c then a= c Transitive property
where is the mistake
a = a Reflexive property
a = b then b = a Symmetric property
a = b and b = c then a= c Transitive property
Okay Suzy....as above...you sorta didn't use the correct Property that helps to answer this problem...in addition in on of the steps...your math is 'incorrect'. But remember...by being incorrect, it is a learning opportunity. I'm going to outline for you the steps one takes to answer these kinds of problems...steps so when you write time on a paper list them from top to bottom...the underlined portions are the parts that are incorrect: Step One: Write the original equation: 2(x + 4) = 18 Step Two: Distributive Property: (2 × x) + ( 2 × 4) = 18 Reasoning: the Coefficient 2 is multiplied to each of the values inside the parenthesis. Step Three: Multiplication Property: (2x) + (8) = 18 Reasoning: 2 times x is 2x and 2 times 4 is eight, 1st problem...you kept the 4, instead of eight. Step Four: Subtraction Property 2x + 8 - 8 = 18 -8 Reasoning: Combining like terms, constants and variables on either side of the equal sign. 18 and 8 are like terms, they are constant. To move 8 from the left side, we subtract 8 from both sides. Step Five: Calculate the difference/Balance the equation: 2x + 0 = 10 Reasoning: Complete Subtraction Property/Differnce. Step Six: Rewrite the Equation 2x = 10 Reasoning: Zero Property and Differnece Step Seven: Division Property 2x ÷ 2 = 10 ÷ 2 Reasoning: 2 is a constant next to a variable, remove the constants and variable to either side. Dividing by 2(which is equal to 1 eliminates coefficient 2), but has to be done on both sides. Step Eight: Reciprocal Property(Property of One): x = 5 Reasoning: 2 ÷ 2 = 1 and since 1 tiimes x is x, 2 can be eliminated on the left side, then the quotient on the right side is completed. Final answer is x = 5 You had your answer as ; x = 7 so, put your answer, 7, into the original equation 2(x + 4) = 18 Step One: 2(7 + 4) = 18 Step Two: 2(11) = 18 Step Three: 22 = 18, but obviously that math statement isn't true 22 ≠ 18 okay, so now check the answer I gave....x = 5 wherever there is an x replace it with 5 Step One: 2(5 + 4) = 18 Step Two: 2(9) = 18 Step Three: 18 = 18 Tah Dah!!! When solving for unknows, when you get your answer, replace your answer into the original equation and if its true on both sides of the equal sign...BINGO!
I know this is a long and drawn out answer to your question...but for each step in solving for unknowns there has to be specific reasons to do things and whatever is done on one side of the equal sign HAS TO BE DONE on the other side of the equal sign. This kind of problem could be solved in 2 or 3 steps, and as you get continue to do these kinds of problems, you will have that kind of skill. Good Luck
Yaro,
The possible properties you listed do not fit your problem. Were these your initial thoughts or are they the answers you have to chose from?
Here is how Suzie should have solved her problem:
2(x + 4 ) = 18
(2*x) + (2*4) = 18 --- using the distributive property of addition she multipled the 2 by BOTH terms within the parenthesis.
2x + 8 = 18 --- subtracting 8 from both sides to keep the equation balanced
2x = 10
x = 5 ---- dividing both sides by 2 leaving the the x to stand alone.
here's a quick reference of math properties that might help you with these assignments.
http://bp025.k12.sd.us/images/Math_Links/ALGEBRAIC%20PROPERTIES%20OF%20EQUALITY2.htm