SOLVING FOR VARIABLES Learn the Simple Algebra of
SOLVING FOR VARIABLES! Learn the Simple Algebra of solving for numerous variables! Lesson A 1. 2. 2 “Finding a Formula”
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WHY DO WE SOLVE FOR VARIABLES? Solving for variables helps us find what we are looking for. When we are saying that we are looking for a number, we replace it with a variable. Using a variable is an easier way to find the number we are looking for. Variable Types. Any Lettero. A o. B o. C… Most commonly used letters are x and y.
Solving for X! Example- X+4=8 Goal: Get X by itself Subtract 4 from each side: X+4=8 -4=-4 Rule: Whatever you do to one side you do to the other. X=8 -4 When 4 was subtracted from the left X was left alone. X=4
SIMPLICITY As you can see, solving for X is quite simple. But problems will of course get harder. The previous example is one of the simplest problems that you can have. Just remember the goal is to get X by itself every time. Let’s try to do some different problems…
SOLVE FOR Y 2 Y-8=2 *Remember the goal is to get Y by itself! +8=+8 (First move the 8 by adding 8 to each side. ) 2 Y=2+8 (Add together 2 and 8. ) 2 Y=10 (2+8 is 10. Now you still want to get Y by itself. ) 2 Y/2=10/2 (Divide by two, because 2 and Y are being multiplied together and division is the opposite of multiplication. ) Y=5 (Dividing by 2 cancels the 2 s, leaving Y alone, and dividing 10 by 2 leaves you with 5!)
JUST A COUPLE RULES When moving a number from one side to another you must do the opposite of each sign. Addition, opposite is subtraction. (Same with subtraction). Multiplication, opposite is division. (Same with division). Raising a number to a power, opposite is taking the root of the number. (Same with taking a root, raise to a number).
MULTIPLE VARIABLES Now that you know how to do simple x and y problems, you can solve for more then one variable, when many are listed. Simply do the same thing when solving, except combine numbers that have the same variable. If you are not solving for the variable, and there is a number with the other variables, just move them accordingly with the variable.
EXAMPLE OF VARIABLE PROBLEM Solve for G(½)G+2 t+6=-4+6 t (½)G+2 t-6=-4(-6)+6 t ; First task to get G by itself…so subtract 6 on both sides. You should then get: (½)G+2 t=-10+6 t Next-Still get G alone, by subtracting 2 t from each side. (½)G-2 t=-10+6 t-2 t You should get: (½)G=-10+4 t Finally the last step to get G alone is the multiply by 2, since G is being divided by 2, and multiplication is the opposite of division. 2(½)G=(-10+4 t)2 You end up with: G=-20+8 t!
From the given equation, express in each term how you would solve for each. A=LW (Area= Length times Width) Solve for both Length and Width you divide Area for the specified variable. Ex. In solving for Length it is L=(A/W) In solving for Width it is W=(A/L) This is handy, because sometimes you may have two variables present and have to find the other, so you need to know how the equations work in reverse. EQUATION FOR AREA!!! You can also solve for a specified variable when given information. Ex.
SOLVING WITH A PICTURE From the given information plug in the values for the area of the rectangle. 12 4 Area= Length x Width Since Area Length times Width, just plug in your given values to find area. A=Lx. W L=12 and W=4 (Define what each variable equals first. ) A=12 x 4 Solve! Area is 48
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1. SOLVE FOR X X+8=4 a. b. c. d. ½ 4 -4 12
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Solving for X! Example- -To go back to quiz question click X+4=8 Goal: Get X by itself Subtract 4 from each side: X+4=8 -4=-4 Rule: Whatever you do to one side you do to the other. X=8 -4 When 4 was subtracted from the left X was left alone. X=4
2. SOLVE FOR X 2 x-7=8 7½ b. 30 c. ½ d. 15 a.
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Solving for X! Example- -To go back to quiz question click X+4=8 Goal: Get X by itself Subtract 4 from each side: X+4=8 -4=-4 Rule: Whatever you do to one side you do to the other. X=8 -4 When 4 was subtracted from the left X was left alone. X=4
3. SOLVE FOR G 6 G+6 t=24 G=84 -36 t b. G=4+t c. G=4 -36 t d. G=4 -t a.
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EXAMPLE OF VARIABLE PROBLEM Solve for G(½)G+2 t+6=-4+6 t (½)G+2 t-6=-4(-6)+6 t ; First task to get G by itself…so subtract 6 on both sides. You should then get: (½)G+2 t=-10+6 t Next-Still get G alone, by subtracting 2 t from each side. ½)G-2 t=-10+6 t-2 t You should get: ½)G=-10+4 t Finally the last step to get G alone is the multiply by 2, since G is being divided by 2, and multiplication is the opposite of division. 2(½)G=(-10+4 t)2 -To go back to You end up with: quiz question click G=-20+8 t!
4. CHOOSE WHICH EQUATION IS THE VOLUME OF A SQUARE. V=Lx. W b. V=Lx. Wx. H c. V=(bh)/2 d. V=2 Lx 2 Wx 2 H a.
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From the given equation, express in each term how you would solve for each. A=LW (Area= Length times Width) Solve for both Length and Width you divide Area for the specified variable. Ex. In solving for Length it is L=(A/W) In solving for Width it is W=(A/L) This is handy, because sometimes you may have two variables present and have to find the other, so you need to know how the equations work in reverse. EQUATION FOR AREA!!! You can also solve for a specified variable when given information. Ex. -To go back to quiz question click
5. SOLVE FOR THE HEIGHT OF THE RECTANGLE (ROUND TO THE NEAREST WHOLE NUMBER IF NECESSARY. ) h 6 12 Total Volume= 360 a. b. c. d. 3 4 5 6
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SOLVING WITH A PICTURE -To go back to quiz question click From the given information plug in the values for the area of the rectangle. 12 4 Area= Length x Width Since Area Length times Width, just plug in your given values to find area. A=Lx. W L=12 and W=4 (Define what each variable equals first. ) A=12 x 4 Solve! Area is 48
6. SOLVE FOR Q (½)Q+12 t=6 t-8+3 r Q=-3 t-4+3/2 r b. Q=-12 t-16+6 r c. Q=-18 t-8+3 r d. Q=-3 t-4+1 r a.
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SIMPLICITY As you can see, solving for X is quite simple. But problems will of course get harder. The previous example is one of the simplest problems that you can have. Just remember the goal is to get X by itself every time. Let’s try to do some different problems… -To go back to quiz question click
7. VOLUME OF THE CYLINDER With the given equation for the volume of a cylinder solve for the radius. r= v/∏h b) r=v/∏h c) r=(v/∏h)2 d) r= v∏h a)
THAT’S WRONG! To go back and reference click. To go back to question click-
THAT’S RIGHT! CONGRATULATIONS! To go back to the beginning click-
From the given equation, express in each term how you would solve for each. A=LW (Area= Length times Width) Solve for both Length and Width you divide Area for the specified variable. Ex. In solving for Length it is L=(A/W) In solving for Width it is W=(A/L) This is handy, because sometimes you may have two variables present and have to find the other, so you need to know how the equations work in reverse. EQUATION FOR AREA!!! You can also solve for a specified variable when given information. Ex. -To go back to quiz question click
8. TRUE OR FALSE? Please answer either true or false to the following question. A variable can be any letter? TRUE or FALSE
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WHY DO WE SOLVE FOR VARIABLES? Solving for variables helps us find what we are looking for. When we are saying that we are looking for a number, we replace it with a variable. Using a variable is an easier way to find the number we are looking for. Variable Types. Any Lettero. A o. B o. C… Most commonly used letters are x and y. -To go back to quiz question click.
9. SOLVING AREA Solve the area of a triangle with the following formula: A= (½)bh a) b) 8 c) d) 12 A=96 A=48 A=192 A=24
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THAT’S RIGHT! CONGRATULATIONS! To go back to the beginning click-
SOLVING WITH A PICTURE -To go back to quiz question click From the given information plug in the values for the area of the rectangle. 12 4 Area= Length x Width Since Area Length times Width, just plug in your given values to find area. A=Lx. W L=12 and W=4 (Define what each variable equals first. ) A=12 x 4 Solve! Area is 48
10. TRUE OR FALSE Please answer true or false to the following question. Division is the opposite of raising a number to a power. TRUE or FALSE
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THAT’S RIGHT! CONGRATULATIONS! (THE OPPOSITE OF DIVISION IS MULTIPLICATION!) To go back to the beginning click-
JUST A COUPLE RULES -To go back to quiz question click When moving a number from one side to another you must do the opposite of each sign. Addition, opposite is subtraction. (Same with subtraction). Multiplication, opposite is division. (Same with division). Raising a number to a power, opposite is take the root of the number. (Same with taking a root, raise to a number).
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