Transcript StAIR: Solving for X

Solving for X
This presentation will guide
you through solving a onestep or two-step equation.
The buttons below will help you move through this
lesson. At any time, use the “left arrow” button to go
back to the previous slide or the “right arrow” to go to
the next slide. Use the “home” button to come back to
the beginning page.
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Solving for X
First choose your starting level.
1.One step equations
2.Two step equations
Solving for X
How to solve a one – step equation
 Object: To solve an equation, you must get
the variable by itself to determine it’s
value.
 To solve for x, you must “undo” the four
operations that we use in everyday
mathematics. Those operations include
addition, subtraction, multiplication, and
division.
 We must also keep the equation balanced.
What we do to one side of the equation,
we have to do to the other side of the
equation. More specifically, the operation
that we perform on the left side of the
equation we have to perform on the right
side of the equation.
 An example of addition in an equation is
X + 4 = 243.
Here we are adding 4 to an unknown
value and it equals 243. To undo addition,
we must use subtraction.
X + 4 – 4 = 243 – 4
In this example, x is equal to 239.
 An example of subtraction in an equation
is
X – 6 = 33.
Here we are subtracting 6 from an
unknown value and it equals 33. To undo
subtraction, we must use addition.
X – 6 + 6 = 33 + 6
In this example, x is equal to 39.
 An example of multiplication in an
equation is
3X = 6.
Here we are multiplying 3 by an unknown
value and it equals 6. To undo
multiplication, we must use division.
3X / 3 = 6 / 3
In this example, x is equal to 2.
 An example of division in an equation is
X / 4 = 12.
Here we are dividing an unknown value by
4 and it equals 12. To undo division, we
must use multiplication.
X / 4 * 4 = 12 * 4
In this example, x is equal to 48.
Let’s try a few examples!
X + 16 = 24
In this example, to solve for X we need to:
A. Add 16 to both sides.
B. Subtract 16 from both sides.
C. Multiply both sides by 16.
D. Divide both sides by 16.
Not quite! Here’s why:
X + 16 = 24
To “undo” addition, we must subtract 16
from both sides of the equation like this:
X + 16 – 16 = 24 –16
Click here to go back to the quiz.
Way to go!
You’re right! To “undo” addition, we must
subtract from both sides of the equation.
X + 16 – 16 = 24 – 16
Try another one!
X – 12 = 36
In this example, to solve for X we need to:
A. Add 12 to both sides.
B. Subtract 12 from both sides.
C. Multiply both sides by 12.
D. Divide both sides by 12.
Not quite! Here’s why:
X – 12 = 36
To “undo” addition, we must subtract 12
from both sides of the equation like this:
X – 12 + 12 = 36 + 12
Click here to go back to the quiz.
Way to go!
You’re right! To “undo” addition, we must
add to both sides of the equation.
X – 12 + 12 = 36 + 12
Try another one!
4X = 32
In this example, to solve for X we need to:
A. Add 4 to both sides.
B. Subtract 4 from both sides.
C. Multiply both sides by 4.
D. Divide both sides by 4.
Not quite! Here’s why:
4X = 32
To “undo” multiplication, we must divide
both sides of the equation by 4 like this:
4X / 4 = 32 / 4
Click here to go back to the quiz.
Way to go!
You’re right! To “undo” multiplication, we
must divide both sides of the equation by
4.
4X / 4 = 32 / 4
Try another one!
X/5=7
In this example, to solve for X we need to:
A. Add 5 to both sides.
B. Subtract 5 from both sides.
C. Multiply both sides by 5.
D. Divide both sides by 5.
Not quite! Here’s why:
X/5=7
To “undo” division, we must multiply both
sides of the equation by 5 like this:
X/5*5=7*5
Click here to go back to the quiz.
Way to go!
You’re right! To “undo” division, we must
multiply both sides of the equation by 5.
X/5*5=7*5
You’ve done great! Now it’s time to try two-step equations.
To go on, click on the right arrow. To go back to the
beginning, click on the home button.
Solving for X
How to solve a two – step equation
 Object: To solve a two-step equation, you
must get the variable by itself to determine
it’s value. However, getting the variable by
itself requires one more step than the
previous equations.
 First, you must move any number that
does not have a variable to the other side
of the equal sign. You do this by “undoing”
addition or subtraction.
 Second, you follow the directions that we
learned before to get the variable by itself.
 An example of a two step equation is
3X + 5 = 17.
Here we are adding 5 to some number
multiplied by three and it equals 17. Our
first step is to undo addition by subtracting
5 on both sides of the equation.
3X + 5 – 5 = 17 – 5
This simplifies to 3X = 12. Next we need
to undo multiplication by dividing both
sides by 3.
3X / 3 = 12 / 3
In this example x is equal to 4.
 Another example of a two step equation is
5X – 4 = 26.
Here we are subtracting 4 from some
number multiplied by five and it equals 26.
Our first step is to undo subtraction by
adding 4 to both sides of the equation.
5X – 4 + 4 = 26 + 4
This simplifies to 5X = 30. Next we need
to undo multiplication by dividing both
sides by 5.
5X / 5 = 30 / 5
In this example x is equal to 6.
Let’s try a few examples!
4X + 16 = 64
In this example, the first step to solve for X
is:
A. Add 16 to both sides.
B. Subtract 16 from both sides.
C. Multiply both sides by 4.
D. Divide both sides by 4.
Not quite! Here’s why:
4X + 16 = 64
First, you must move any number that
does not have a variable to the other side
of the equal sign. You do this by
subtracting 16 from both sides of the
equation like this:
4X + 16 – 16 = 64 – 16
Click here to go back to the quiz.
Way to go!
You’re right! First, you must move any
number that does not have a variable to
the other side of the equal sign. You do
this by subtracting 16 from both sides of
the equation like this:
4X + 16 – 16 = 64 – 16
Let’s work on the second step..
4X + 16 – 16 = 64 – 16
In this example, the second step to solve for
X is:
A. Add 16 to both sides.
B. Subtract 16 from both sides.
C. Multiply both sides by 4.
D. Divide both sides by 4.
Not quite! Here’s why:
4X + 16 – 16 = 64 – 16
This simplifies to 4x = 48. Next we need to
undo multiplication by dividing both sides
by 4.
4X / 4 = 48 / 4
Click here to go back to the quiz.
Way to go!
You’re right! Next we need to undo
multiplication by dividing both sides by 4.
4X / 4 = 48 / 4
In this example, x is equal to 12.
Try another one!
6X – 8 = 58
In this example, the first step to solve for X
is:
A. Add 8 to both sides.
B. Subtract 8 from both sides.
C. Multiply both sides by 6.
D. Divide both sides by 6.
Not quite! Here’s why:
6X – 8 = 58
First, you must move any number that
does not have a variable to the other side
of the equal sign. You do this by adding 8
to both sides of the equation like this:
6X – 8 + 8 = 58 + 8
Click here to go back to the quiz
Way to go!
You’re right! First, you must move any
number that does not have a variable to
the other side of the equal sign. You do
this by adding 8 to both sides of the
equation like this:
6X – 8 + 8 = 58 + 8
Let’s work on the second step..
6X – 8 + 8 = 58 + 8
In this example, the second step to solve for
X is:
A. Add 8 to both sides.
B. Subtract 8 from both sides.
C. Multiply both sides by 6.
D. Divide both sides by 6.
Not quite! Here’s why:
6X – 8 + 8 = 58 + 8
This simplifies to 6x = 66. Next we need to
undo multiplication by dividing both sides
by 6.
6X / 6 = 66 / 6
Click here to go back to the quiz.
Way to go!
You’re right! Next we need to undo
multiplication by dividing both sides by 6.
6X / 6 = 66 / 6
In this example, x is equal to 11.