SOL 7.13, 7.14, 7.15
SOL 7.13: The student will
a) write verbal expressions as algebraic expressions and sentences as equations and vice versa; and
b) evaluate algebraic expressions for given replacement values of the variables.
**Use PEMDAS when solving any algebraic expression s.
Parentheses, Exponents, Multiply or divide (whichever comes first), Add or subtract (whichever comes first)
A variable is a letter or symbol that represents an unknown value. When variables are used with other numbers,
parenthesis, or operations they create an algebraic expression. A coefficient is the number multiplied by the variable in
an algebraic expression. A term is the name given to a number, a variable, or a number and a variable combined by
multiplication or division. A constant is a number that cannot change its value.
Example: 12a – 6b + 4
coefficient: 12, -6
constant: 4
variable: a, b
terms: 12a, -6b, 4
 You can translate word phrases into variable expressions.
 Examples:
 Three more than a number = x + 3
 The quotient of a number and 8 = y/8
 Six times a number = 6 x n or 6n
 15 less than a number = z – 15
 The quotient of 30 and a number plus 10 = 30/x + 10.
Key words to look for:
 Addition: Add, Plus, Sum, Total, Increased by, More than, Greater than, Altogether, In all
 Subtraction: Minus, Difference, Subtract, Less than, Decreased by, Less, Take away, How many more/left,
Borrowed, Diminished by
 Multiplication: Product, Times, Multiply, Of, Twice/double, Triple, Repeated, Squared, Cubed, Power of, Factors
 Division: Quotient, Divide, Divided by, Split Equally, Each, Square Root, Per
 Multiplication expressions should be written in side-by-side form, with the number always in front of the
variable. Ex: 3a
2t
1.5c
 Division expressions should be written using the fraction bar instead of the traditional division sign.
3
𝑡
𝑐
Ex: 𝑥
5
2
SOL 7.14: The student will
a) solve one- and two-step linear equations in one variable; and
b) solve practical problems requiring the solution of one- and two-step linear equations.
An equation is a statement that says two amounts are equal. Think of an equation as a scale: Whatever you do to one
side, you must do to the other side to keep it balanced.
To solve an equation means to find the value of the variable that makes the equation true. To do this you must get the
variable on one side of the equation by itself.
To solve a one step equation you must do the opposite operation.
𝑡
EX) x + 7 = -9
u – 3 = 12
7y = -42
=2
5
-7 -7
+ 3 +3
7
7
x5 x5
X = -16
u = 15
y = -6
t = 10
A two step equation is an equation that requires two steps (operations) to solve.
Steps for Solving Two-Step Equations:
1. Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both
sides of the equation.
2. Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of
the equation.
The first step will always be either adding or subtracting. The second step will always be either multiplying or dividing.
Helpful Hints:
 Identify what operations are on the variable side. (Add, Sub, Mult, Div)
 “Undo” the operation by using opposite operations.
 Whatever you do to one side, you must do to the other side to keep equation balanced.
Ex: 8x + 5 = 21
-5 -5
8x = 16
8
8
X=2
b/3 + 4 = 9
- 4 -4
b/3 = 5
x3 x3
b = 15
Word Problems:
Ex) A bike shop rents mountain bikes for a $8.50 insurance charge plus $3.50 per hour. For how
many hours can a person rent a bike with $33?
8.50 + 3.50h = 33
- 8.50
-8.50
3.50h = 24.50
3.50
3.50
h =7
Ex) Ravi will be four times John’s age after five years. John is 12. How old is Ravi?
4(12) + 5 = x
48 + 5 = x
53 = x
SOL 7.15: The student will
a) solve one-step inequalities in one variable; and
b) graph solutions to inequalities on the number line.
An inequality is a mathematical statement in which two quantities are NOT EQUAL.
< less than, >greater than, < less than or equal to, > greater than or equal to
Graphing an inequality means showing all of the possible solutions to an inequality. We graph inequalities on a number
line. Open circle means < or >, a closed circle means < or > to include the number.
Ex) x > 4
x < -2
Solving an inequality is just like solving an equation except you have an inequality sign instead of an equals sign; then
you graph the solution.
EX) x + 6 < 12
x–3> 5
-6 -6
+3 +3
X < 6 -2 -1 0 1 2 3 4 5 6 7 8 9 10 111213141516 x > 8
-2 -1 0 1 2 3 4 5 6 7 8 9 101112131415
There is a special case: When you multiply or divide by a NEGATIVE number, you flip the inequality sign.
EX) -6x < 12
-6
-6
X > -2
𝑐
−2
-5 -4-3-2-10 1 2 3 4 5 6 7 8 9 10111213
>4
x-2 x-2
c < -8
-10-9 -8 -7-6-5-4-3 -2 -1 0 1 2 3 4 5 6 7 8