Bellwork 9-14-15

Unit 1 Quiz Sept 2015Simplify each expression #1-5. Write the problem and answer.

1: -½ ( ¼ x + 10)2: 8y – 2x + y + 5y3: 9ab + 3a2 + 5ab + 4a2

4: (2x2y + 4xy – 7) – (3x2y – 7xy + 10)5.

6: (Do not have to copy problem.) If a rectangle has length x2+4, and the width is shorter by 3, what is the perimeter?

Bellwork Solutions 9-14-15

Definition: Linear Equation

Let a and b be real numbers such that a ≠ 0. A linear equation in one variable is an equation that can be written in the form

ax + b = 0

Linear Equations in One Variable

• An equation is a statement that indicates that two quantities are equal. It must have an equal sign separating two parts.

• A solution to an equation is a value of the variable that makes the equation a true statement.

• Substituting a solution to an equation for the variable makes the right-hand side equal to the left-hand side.

Linear Equations in One Variable

Equation Solution Check

x = -4 -4 (-4) = -4

p + 3 = 11 8 (8) + 3 = 11

-2b = -20 10 -2(10) = -20

Addition & Subtraction Properties of Equality

Let a, b, and c represent real numbers.

Addition property of equality: If a = b, then a + c = b + c.

Subtraction property of equality: If a = b, then a - c = b - c.

Multiplication & Division Properties of Equality

Let a, b, and c represent real numbers.

Multiplication property of equality:If a = b, then a • c = b • c.

Division property of equality:If a = b, then a/c = b/c (provided c ≠ 0).

Procedure for Solving a Linear Equation in One Variable

Step 1: Simplify both sides of the equation.a) Clear parentheses.b) Consider clearing fractions or decimals (if any are

present) by multiplying both sides of the equation by a common denominator of all terms.

c) Combine like terms.

Procedure for Solving a Linear Equation in One Variable

Step 2: Use the addition or subtraction property of equality to collect the variable terms on one side of the equation.

Step 3: Use the addition or subtraction property of equality to collect the constant terms on one side of the equation.

Procedure for Solving a Linear Equation in One Variable

Step 4: Use the multiplication or division property of equality to make the coefficient of the variable term equal to 1.

Step 5: Check your answer!

9-14-15 HW – Lesson 1.41 step equations. Solve for the

variable. Show work!1. 12 + x =402. -3/5 p = 4/153. 4 = w/2.24. -x = 65. -6/5 y = -3/56. 5 = t/167. -a = -2

Mon. 9-14-15 HW Problems Solutions 1step equations

• 1. x=28• 2. p= -4/9• 3. 8.8=w• 4. x= -6• 5. y= ½• 6. 80=t• 7. a=2

Wedn. 9-17-14 Homework

Intermediate Algebra textbook pp. 46-47 #15-25 odds

Complete before leaving or can be found on website: uhstitans.com/carruthers-latrease

Bellwork 9/18

• Show the “check” work to see if the solution is correct.

3(y – 4) = 2y – 5 y = - 7

Warm Up 9/18

Solve the equation:

¼ w + 1/3 w – 1 = ½ (w – 4)

Remember: the fractions in this equation can be eliminated by multiplying both sides of the equation by any common multiple of the denominators.