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Enter a set of expressions, e.g. ab^2,a^2b

Enter equation to solve, e.g. 2x+3=4

Enter equation to graph, e.g. y=3x^2-1

Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

Solve for:

Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

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APPLICATIONS OF LINEAR EQUATIONS

Key Words:

• Addition - sum, added to, increased by, more than

• Subtraction - difference, minus, decreased by, subtracted from

• Multiplication - product, times, double (2x), tripled (3x)

• Division - quotient, ratio, divided by

Formulas:

• Area of square:

• Area of a rectangle:

• Area of a triangle:

• Area of a trapezoid:

• Area of a circle:

• Perimeter:

In other words, add each side together.

• Circumference of a circle:

Angle Properties:

• Vertical Angles are opposite angles formed by intersecting lines. Vertical angles always have the
same measurement.

• Complementary Angles are two angles whose sum is 90°.

• Supplementary Angles are two angles whose sum is 180°.

Common Mistakes to Avoid:

• For perimeter, be sure to add EACH AND EVERY side in the formula.

• Be very careful to translate the problem into correct mathematical form. When it has been translated,
you should be able to read it back.

• Be careful: a minus b is translated a - b; whereas, a less than b is translated b - a.

• Be careful on the difference between these two statements:

- The sum of four times a number and 5 is translated 4x + 5.

- Four times the sum of a number and 5 is translated 4(x + 5).

• Make sure that you answer the question being asked. If it asks for two answers, give both.

PROBLEMS

1. The sum of four and twice a number is 46.
Find the number.

Let x = the number.

3. A number decreased by 15 is 123. Find the
number.

Let x = the number.

2. Three times the sum of nine and a number
is 48. Find the number.

Let x = the number.

4. If seven is subtracted from a number and this
difference is doubled, the result is four more
than the number. Find the number.

Let x = the number.

5. If the quotient of three times a number and
four is decreased by three, the result is ten.
Find the number.

Let x = the number.

7. A stained-glass window in a church is in the
shape of a square. The perimeter of the
square is eight times the length of a side in
feet, decreased by twelve. Find the length of
a side of the window.

Let

s = the length of one side of the
square window

4s = perimeter of the window

6. A 19 foot piece of string is cut into two
pieces so that one piece is five feet shorter
than twice the shorter piece. Find the length
of both pieces.

Let

x = the shorter piece
2x - 5 = the longer piece

8. The length of a rectangular shaped garden
is five feet more than twice the width. The
perimeter is 58 feet. Find the length and
width of the garden.

Let

w = the width of the garden.
2w + 5 = the length of the garden.

9. A lot is in the shape of a triangle. One side
is 32 feet longer than the shortest side while
the third side is ten feet shorter than twice
the shorter side. The perimeter of the lot is
238 feet. Find the length of the sides of the
lot.

Let

x = the shortest side.
x + 32 = the second side.
2x - 10 = the third side.

10. The supplement of an angle measure 15°
more than four times its complement. Find
the measure of the angle.

Let

x = the degree measure of the angle.
180 - x = the degree measure of supplement.
90 - x = the degree measure of complement.