Download Equations

Name _______________________________________ Date __________________ Class __________________
Multi-Step Equations
Section A Family Letter: Solving Linear Equations
Dear Family,
The student will learn how to combine like terms in order to
simplify an expression. The student will learn that although
combining like terms changes the way an expression looks,
the value of the expression stays the same. For example:
Combine like terms.
6x  8y  9x
6x  8y  9x
6x  9x  8y
15x  8y
Identify like terms.
Rearrange the expression.
Add the coefficients of like terms.
The student will also learn to solve equations where there is
more than one variable term on the same side of an equation
by using the Distributive Property.
Solve. 3k  5  k  9
3k  5  k  9
2k  5  9
2k  5  9
5 5
2k  14
2k 14

2
2
k  7
Combine “like terms.”
3k  k  2k
Now get the k alone.
Subtract first.
Divide next.
In both math and science, there are times when a common
equation is easier to use if a certain variable is alone on one
side of the equal sign.
Solve d  r  t for t.
drt
d r t

r
r
d
d
 t OR t 
r
r
Vocabulary
These are the math
words we are learning:
equivalent expressions
expressions that have
the same value for all
the values of the
variables
like term terms that
have the same variable
raised to the same
exponent
literal equation an
equation with two or
more variables
simplify perform all the
operations possible,
including combining like
terms
solution of a system
of equations a set of
values making all
equations in a system
true
system of equations
a system of two or more
equations that contain
two or more variables
term elements of an
expression that are
separated by plus or
minus signs
Divide both sides by r.
The t is now alone.
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Multi-Step Equations
Section A Family Letter: Solving Linear Equations continued
The student will also learn to solve equations with variables on both
sides of the equal sign using inverse operations to get all the
variables on one side and then solve.
Solve. 6y  5  3  4y
6y  5  3  4y
4y
4y
Get all y’s on one side by
subtracting 4y from both sides.
2y  5  3
2y  5  3
5 5
2y  8
2y 8

2 2
y4
Add 5 to both sides.
Divide both sides by 2.
The student will be introduced to systems of equations and learn how to find the
values that make a system true. The first method gets the same variable alone in both
equations. Then the equations are set equal to each other and solved for the value of
the other variable. Finally, the value found is substituted into either equation to find the
value of the first variable.
Solve the system of equations.
x  3y  5
3y 3y
x  2y  3
2y 2y
x  5  3y
x  3y  5
x  2y  3
Get the x by itself in
both equations.
x  3  2y
5  3y  3  2y
Set x  x.
5  3y  3  2y
3y
3y
Simplify and solve for y.
53y
53y
3 3
2y
x  3(2)  5
Subtract 3 from both
sides.
Substitute 2 into either
equation for y to find the
value of x.
x65
x  1
Solution: (x, y)  (1, 2)
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Multi-Step Equations
Section A Family Letter: Solving Linear Equations continued
In the second method, the student will solve one equation for a
variable, then substituting the resulting expression into the second
equation.
It is important that the student learn to solve equations. He or she
will use this skill in every math course he or she takes from this point
forward.
Sincerely,
Ms. Galanis
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Multi-Step Equations
Section A At-Home Practice: Solving Linear Equations
Combine like terms.
1. 3x  6v  5x  3v  8
2. 4s  3s  2  5j  9s  7j
_______________________________________
________________________________________
Solve. Check each answer.
3. 9n  5  3n  5
_______________________
6. 5(2w  1)  w  49
_______________________
9. 13h  45  2h
_______________________
12. 4(n  5)  9n
_______________________
4. 8p  9  6p  7  2
5.
________________________
________________________
7. 15x  9  2x  30
8.
________________________
10. 8  6k  10  24
3 2p 15


7 7
7
________________________
11. 4(x  5)  15  x
________________________
13. 21  3b  11b  7
d 1 14
 
5 5 5
________________________
14. 2(5  3x)  4(2x)
________________________
________________________
15. The equation P = IV gives the power P of an electrical circuit, where I is the current
and V is the voltage. Solve this equation for V.
________________________________________________________________________________________
Solve each system of equations.
16. y  3x  9
y  7x  19
17. 3x  9y  9
x  2y  7
_______________________________________
18. 9x  3y  6
2x  y  3
_______________________________________
20. 2x  4y  6
x  2y  2
_______________________________________
________________________________________
19.
xy3
2x  3y  1
________________________________________
21. 6x  9y  12
4x  6y  8
________________________________________
Answers: 1. 8x  3v  8 2. 10s  12j  2 3. n  0 4. p  1 5. d  15 6. w  4 7. x  3 8. p  6 9. h  3 10. k  7
P
11. x  1 12. n  4 13. b  2 14. x  5 15. V 
16. (1, 12) 17. (3, 2) 18. (5, 13) 19. (2, 1) 20. no solution
I
21. infinite number of solutions
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Multi-Step Equations
Family Fun: Four in a Row Equations
Directions
 Each player should create a 4by4 grid as shown.
 Have each player write the equations below in any order
in each one of the squares in the grid.
x0
x1
x2
x3
x5
x6
x7
x8
x  1
x  2
x  3
x  4
x  5
x  6
x  7
x4
 Each player will work out problems 1 to 16 in the order in
which they appear. If the player finds the solution on his
or her grid, the player will color in the corresponding
square.
 The first player to color in four squares in a row, column,
or diagonal wins the game.
1. 5x  1  15  1
2. 3  5  2x
3. 3x  4x  8
4. 11(x  4)  44
5. 23  4x  3x  5
6. 7x  1  3x  9
7. 15x  1  13x  15
8. 3(x  4)  5x
9.
5x 12 2


7
7 7
11. 9(2x)  4x  21  3x  23
13.
2x  60
 3x
4
15. 5  (x  2)  2x  2
10.
x8
 3
3
12. 2x  1  4x  7
14.
3 x 10
 
8 8 8
16. 2x  5  x
Answers: 1. x  3 2. x  1 3. x  8 4. x  0 5. x  4 6. x  2 7. x  7 8. x  6 9. x  2 10. x  1 11. x  4
12. x  3 13. x  6 14. x  7 15. x  5 16. x  5
Holt McDougal Mathematics