August 28, 2016
August 28, 2016
Vocab
equation a mathematical sentence that states that two expressions are
equivalent
equivalent expressions expressions that may look different but have the same value
inverse operations two operations that "undo" each other. For example: addition and
subtraction
like terms terms with the same variables and the same corresponding exponents
simplify to make an expression as simple as possible
solution a value that makes the statement true
solve to find the value of a variable in an equation that makes the equation
true (ie isolate the variable)
August 28, 2016
Solve 2.5x − 13 = 2. Check your solution.
x=6
?
Solve −12 = 9x − 6x + 15. Check your solution.
x = -3
?
August 28, 2016
Solve the equation. Check your solution.
1. −2n + 3 = 9
2.
3. −2x − 10x + 12 = 18
August 28, 2016
Solve 2(1 − x) + 3 = − 8. Check your solution.
x=
?-6.5
2 - 2x + 3 = -8
OR
2(1 - x) = -11
1 - x = -5.5
5 - 2x = -8
-2x = -13
-x = -6.5
x = 6.5
x = 6.5
homework symbol
Distributive Property (ie life guard property)
For every real number a, b, and c ...
a(b + c) = ab + ac
a(b - x) = ab - ac
August 28, 2016
Solve the equation. Check your solution.
4. 3(x + 1) + 6 = −9
5. 15 = 5 + 4(2d − 3)
6. 13 = −2(y − 4) + 3y
7. 2x(5 − 3) − 3x = 5
8. −4(2m + 5) − 3m = 35
9. 5(3 − x) + 2(3 − x) = 14
August 28, 2016
Exit Ticket: Solve 8x + 9 − 4x = 25. Check your solution.
Pg 16: 1, 2, 4 – 34e, 35 – 37, 39 – 42, 47, 49 – 51, 57 -­‐ 65
August 28, 2016
August 28, 2016
Simplify the expression.
1. (2x2 − 6x) − (−2x2 + 3x)
2. (5a2 − a) − (2a2 − 5a)
3. (4y2 + y) − (6y2 − 5y)
4. (−2d 2 − d) − (5d 2 − 5d)
5. (2h2 + 5z) + (2h2 + 9z)
6. (2y2 + 9xy) + (3y2 − 2xy)
August 28, 2016
How can you use multi-step equations to solve real-life problems?
August 28, 2016
Work with a partner. The sum S of the angle measures of a polygon
with n sides can be found using the formula S = 180(n − 2). Write and
solve an equation to find each value of x. Justify the steps in your
solution. Then find the angle measures of each polygon. How can you
check the reasonableness of your answers?
x =?750
x =?1000
x =?400
August 28, 2016
Work with a partner.
a. Draw an irregular polygon.
b. Measure the angles of the polygon. Record the measurements on a
separate sheet of paper.
c. Choose a value for x. Then, using this value, work backward to
assign a variable expression to each angle measure, as in Exploration
1.
d. Trade polygons with your partner.
e. Solve an equation to find the angle measures of the polygon your
partner drew. Do your answers seem reasonable? Explain.
August 28, 2016