UNIT 2
NAME______Solving Equations
Warm-up: (Day 1)
1.Evaluate the expression 3ab-c2 when a=3, b=4, c= -5 / 2. Evaluate:a. 42 b. 16 c. 3-2 d. 19
3. What is the additive inverse of -13? / 4. What is the multiplicative inverse of 23?
To solve any linear equation, follow these steps:
1. Draw a vertical line (up & down) through the equal sign.
2. Get rid of an parenthesis using the distributive property. (GO FISHING)
3. Combine Like Terms
4. Use inverse or opposite operations (or sign) to get the variable alone. (what you do to 1 side you do to the other)
5. Check: 1. Substitute 2. Simplify
Solving 1-Step Equations: (Day 1)
To be an equation you need an ______sign.
Inverse operations
1. The inverse or opposite operation of addition is ______. The inverse or opposite operation of subtraction is ______.
2. The inverse or opposite operation of multiplication is ______. The inverse or opposite operation of division is ______.
3. The inverse or opposite operation of squaring is taking the ______.
Examples
1. p + 4 = -12 Check 2. 3t=15 Check 3. 7=x - 23 Check
4. x2= 5 Check 5. 4a = 24 Check 6. x2= 9 Check
Try these:
7. 8 + q = -11 Check 8. 6 = a3 Check 9. 45 = 9x Check
10. N – 60 = -50 Check 11. 49 = m2 Check 12. K – 3.2 = 5.8 Check
START HOMEWORK #1
Warm-up: (Day 2)
1.Evaluate the expression 4[2-(2+3)]6 / 2. Write in scientific notation: .00000004433. Name the property: 4+(3+7)=(4+3)+7 / 4. Write the expression 3.5 x 107 in expanded form.
Solving 1-Step Equations: (with Decimals & Fractions) (Day 2)
1. 10 = t - 20.7 Check 2. 1.8 + t = -36 Check 3. 1.5s = -7.5 Check
4. -g +(-4) = -20 Check 5. r-5 = 15.5 Check 6. m2 = .01 Check
Try These:
7. x + -.5 = 1.3 Check 8. .07 = 21p Check 9. n.2=-7 Check
10. f2 = .16 Check 11. -8.7+ r = - 16.9 Check 12. 80n = 4.5 Check
Solving Equations with Fractions
Change all fractions to decimals if possible (neat): in calc.
13. 34 + y = 12 Check 14. j - 12 = 312 Check 15. x – 13 = 15 Check
Try These:
16. j-110 =5 Check 15. 26+m=45 Check 16. x-16=4.6 Check
Start Homework #2
Warm-up: (Day 3)
1. What is the multiplicative inverse of 15 ? / 2. Find the reciprocal of the following:a. 13 b. -56 c. 16 d. 35 e. 7
3. What does finding the reciprocal of a number
mean? / 4. Write each fraction as a decimal if it is not repeating.
a. 13 b. -56 c. 16 d. 35 e. -64
Solving 1-Step Equations: (with Fractional Coefficients) (Day 3)
A ______is the number a variable is multiplied by.
1. The coefficient of x in the term 3x is ______. 2. The coefficient of a in the term 12a is ______.
3. The reciprocal of the coefficient of 16m is ______. 4. Is the decimal .625 repeating or non-repeating?
1. 23w=30 Check 2. 45q=60 Check 3. 78z=-56 Check
4. 14b=3 Check 5. 21=15q Check 6. -6=18z Check
Try These:
7. 15k=20 Check 8. 112d=-3 Check 9. -75=12x Check
10. -116b=-4 Check 11. 17h=-12 Check 12. -6=18z Check
13. b5=125 Check 14. -45=12 Check 15. 13=1213n Check
16. The sum of a number and 12 is 48. What is the number? 17. The quotient of a number and 2 is 8. Find the number.
(Start HW #4)
Solving 2-Step Equations: (Day 4)
This is a 2-step equation: 4x-16=20
Move the easy stuff away 1st!!
1. Move anything being ______or ______to the variable first by ______
or ______on both sides.
Now you have a one step equation!!
2. Move anything being ______or ______next by ______or
______on both sides.
Examples:
1. 2x+5=10 Check: / 2. 3x-7=25 Check: / 3. 75=11+16x Check:5. x3+4=13 Check: / 6. 15=b7-8 Check: / 7. 9d-12=1723 Check:
Try These:
1. 2x+5=10 Check: / 2. 3x-7=25 Check: / 3. 75=11+16x Check:8. x3+4=13 Check: / 9. 15=b7-8 Check: / 10. 9d-12=1723 Check:
If time:
1. 4 more than 5 times a number is 34. What is the number? / 2. 2 times a number is added to 7. The result is 15. Find the number.(Start Day 4 Homework)
Equations Matho!!! (Day 5)
Warm-up: (Day 6)
1. Solve & check: 8.6=c-.2 / 2. Evaluate: 3-7-43. Fill in the value of the variable using what you know about properties of real numbers.
a. 3n=1 b. -3+x=0 c. -23+m=-23
n=____ x=____ m=_____ / 4. Solve for the give variable
a. x2=49 b. 3+b2=24
Pythagorean Theorem (Day 6)
The Pythagorean theorem is used to find a ______of a ______triangle when you are given the other ______.
Use the Pythagorean theorem to find the missing side:
1. / 2. / 3.4.
/ 5.
/ 6.
Try these: If necessary, round your answer to the nearest tenth.
1. / 2. / 3.4. / 5 / 6.
Start Homework #6
Warm-up: (Day 7)
1. Evaluate a2+b2 when a = 21 and b = 28 / 2. What is the square root of 925?3. Given the 3 sides of a triangle, tell whether the 3 sides create a right triangle. (hint: it must “fit” into the Pythagorean theorem formula)
a2+b2=c2
a. 2, 3, 4 / b. 4, 6, 8 / c. 5, 7, 10 / d. 16, 24, 32
Pythagorean Theorem Word Problems: (diagrams given) (Day 7)
1. Decide what what side of the triangle in the problem is the hypotenuse (C).
2. Substitute for a, b, and c into a2+b2=c2.
3. Solve for a, b, or c.
4. ANSWER THE QUESTION!!
1. What is the value of x, in inches, in the right triangle below? Show Work1) 15 2) 8 3) 34 4) 4
2. Tanya runs diagonally across a rectangular field that has a length of 40 Show Work
yards and a width of 30 yards, as shown in the diagram below. What is the
length of the diagonal, in yards, that Tanya runs?
3.Don placed a ladder against the side of his house as shown in the diagram below. Show Work
Find the distance from the foot of the ladder to the base of the house.
(round your answer to the nearest foot)
Try These:
1. The end of a dog's leash is attached to the top of a 5-foot-tall fence post, as shown in the Show WorkDiagram below. The dog is 7 feet away from the base of the fence post.
2. Nancy’s rectangular garden is represented in the diagram below. Show Work
If a diagonal walkway crosses her garden, what is its length, in feet?
3. The length of the hypotenuse of a right triangle is 34 inches and the length of one of its Show Work
legs is 16 inches. What is the length, in inches, of the other leg of this right triangle?
(Start Day 7 Homework)
Warm-up: (Day 8)
1. Solve for x .04x-.8=1.6 Check / 2. Solve for s: 12s=15 Check3. Brent balance in his bank account was $210.50 on Monday. On Thursday he withdrew $47.29 to buy a used skateboard from his neighbor. On Friday he got paid and put 12 of his $400 paycheck into his bank account. What is his balance after he makes the deposit? (show all steps you took to find your answer)
Pythagorean Theorem Word Problems: (diagrams not given) (Day 8)
1. Draw the picture & label sides with correct lengths.
2. Decide what side of the triangle in the problem is the hypotenuse (C).
2. Substitute for a, b, and c into a2+b2=c2.
3. Solve for a, b, or c.
4. ANSWER THE QUESTION!!
(Round your answers to the nearest whole number where necessary)
1. If the length of the legs of a right triangle are 9 and 7, what is the length of the hypotenuse? / Draw Picture2. If the length of a rectangular television screen is 8 inches and its height is 15 inches, what is the length of its diagonal, in inches? / Draw Picture
3. How many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will reach a point on the house 36 feet from the ground? / Draw Picture
4. A cable 20 feet long connects the top of a flagpole to a point on the ground that is 16 feet from the base of the pole. How tall is the flagpole? / Draw Picture
Try These: (round all answers to the nearest tenth where necessary)
1 If the length of the legs of a right triangle are 5 and 7, what is the length of the hypotenuse? / Draw Picture2. If the length of a rectangular television screen is 20 inches and its height is 15 inches, what is the length of its diagonal, in inches? / Draw Picture
3. An 18-foot ladder leans against the wall of a building. The base of the ladder is 9 feet from the building on level ground. How many feet up the wall, to the nearest tenth of a foot, is the top of the ladder / Draw Picture
4. The "Little People" day care center has a rectangular, fenced play area behind its building. The play area is 30 meters long and 20 meters wide. Find, to the nearest meter, the length of a pathway that runs along the diagonal of the play area / Draw Picture
Start Homework #8
Warm-up (Day 9)
1. Write the expression 4.3x10-5in expanded form. / 2. Write the number .00000234 in scientific notation.3. Complete the table:
# of ants / 2 / 7 / 9
# of legs / 12 / 36 / 54 / 72
/ 4. What is the value of 12-2
Solving Equations (with like terms) (Day 9 )
- = + =
6 flowers - 4 flowers = 2 flowers 3 flowers + 2 balloons = 3flower + 2ballons
So…. 6f-4f=2f So….3f+2b=3f+2b
Rule: - Always combine ______terms.
a. Like Terms: 2t, 3t, ______
b. Unlike Terms: 4r, 6y, ______
Simplify by combing like terms:
1. 2b+5b / 2. 12x-6x+7 / 3. 5-8+3y4. 41u-7u-33-22 / 5. 3m-7+8-9m / 6. 71x+63y-23x-14xy
Review: Solve all equations by using ______operations……but first ______like terms.
1. g±13=4+8 / Check: / 2. p-2p=27 / Check:3. 3s-2s=1.5+24 / Check: / 4. 9x-5x+9=1 / Check:
Try These:
1. 9x-5x+9=1 / Check: / 2. 5x+2x-17=53 / Check:3. 2y-8y+29=5 / Check: / 4. 8x-21-5x=-15 / Check:
5. 15+5=x+x-6 / Check: / 6. 18=-6x+8x+8 / Check:
7. 5x-15-30=10 / Check: / 8. .3a+.2a-.5+.2a+.4=1.3 / Check:
Warm-up: (Day 10)
1. What property is illustrated by the equation:2a+b=2a+2b / 2. Simplify: 7(b-6)
3. Write .000000034 in scientific notation. / 4. Simplify: 33b-4-2(4b-8)
Solving Equations (using the distributive property) (Day 10 )
Remember
1. Draw a vertical line (up & down) through the equal sign.
2. Use distributive property to get rid of the parenthesis (GO FISHING!!)
2. Combine Like Terms
4. Use inverse or opposite operations (or sign) to get the variable alone.
(what you do to 1 side you do to the other)
6. Check: 1. Substitute 2. Simplify
1. 5x+2=20 / Check: / 2. 3y-9=30 / Check:3. 30=-(10-y) / Check: / 4. 25-2t-5=19 / Check:
5. 32b+1-7=50 / Check: / 6. 5m-2m-5=17 / Check:
7. x-12-x=38 / Check: / 8. 348+4x-136x+3=9 / Check:
Try These:
1. 63c-1=-42 / Check: / 2. 4c+1=32 / Check:3. 55=4+3(m+2) / Check: / 4. 18=-6+4(2x+3) / Check:
5. 28y-63y-5=40 / Check: / 6. 7r-6r-5=7 / Check:
If there is time:
1. A salesman receives a weekly salary of $150. He also receives $4 for each tire he sells. One week, he earned $330. How many tires did he sell that week? / 2. The sum of 7 times a number and 5 is -51. Find the number.Warm-up: (Day 10)
1. What property is illustrated by the equation:2+7+9=2+7+9 / 2. Simplify: 15-32+6-3
3. If x=-4 and y=3, what is the value of x-3y2 / 4. Which number is irrational?
1) 9 2) 8 3) 0.3333 4. 23
What makes it irrational?
Solving Equations (with variables on both sides) (Day 10 )
Remember
1. Draw a vertical line (up & down) through the equal sign.
2. Use distributive property to get rid of the parenthesis (GO FISHING!!)
2. Combine Like Terms
4. Move all variables to one side, then all numbers to the other. (using inverse operation or sign)
(Tennis Match)
5. Use inverse or opposite operations (or sign) to get the variable alone.
(what you do to 1 side you do to the other)
7. Check: 1. Substitute 2. Simplify
1. 7x=10+2x / Check: / 2. y=4y+30 / Check:3. 0.8m=0.2m+24 / Check: / 4. 7r+10=3r+50 / Check:
5. x+4=9x+4 / Check / 6. c+20=55-4c / Check:
Try These:
1. 9x=44-2x / Check: / 2. 2d=33+5d / Check:3. 8y=90-2y / Check: / 4. 5a-40=3a / Check:
5. .5m-30=1.1m / Check: / 6. 4y+20=5y+9 / Check:
7. 2d+36=-3d-54 / Check: / 8. 2y+5y-5=9y+29 / Check:
Start Day 10 Homework
Warm-up: (Day 11)
1. What property is illustrated by the equation:123X+0=123X / 2. Complete the table:
INPUT / 3 / ? / 8 / 12 / ?
OUTPUT / -4 / -7 / 1 / ? / 7
Name the Rule: y = ______
3. Solve for x: 14x-16=12x / 4. A rental car company charges 195 for the week in addition to 39cents per mile. If Ron’s bill is $285 for the week, about how many miles did Ron drive?
Solving Equations (with variables on both sides & ponds!!!) (Day 11 )
Remember
1. Draw a vertical line (up & down) through the equal sign.
2. Use distributive property to get rid of the parenthesis (GO FISHING!!)