TOPIC 1-1 SOLVING EQUATIONS & INEQUALITIES



TOPIC 1-1 SOLVING EQUATIONS

1) Solve: x + 5 = 21 2) Solve: 32 – r = 16

3) Solve: [pic]n = 12 4) Solve: [pic]x – 2 = -37

5) Solve: 10b – 6b – 3 = 9 6) Solve: 5(x + 3) = -30

7) Solve: 5x – 21 = -2x + 28 8) Solve: -3n – 2(n + 4) = -6n – 5

NAME_________________________DATE_____________PER.______

SOLVING EQUATIONS

Solve each of the following. Work must be shown to receive credit.

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|q – 17 = 23 |2. 61 – p = 14 |

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|3. [pic]b = 25 |4. [pic]w = 75 |

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|3x – 9 = 0 |6. [pic]x – 15 = 10 |

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|6(3 – e) = 42 |8. 13x – 7x = 24 |

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|15(2 + x) – 3x = 114 |10. 2(x – 8) – 3(x + 2) = -24 |

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Review 1-2: SOLVING QUADRATIC EQUATIONS

|TERM: |DEFINITION: |SKETCH: |

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|Quadratic Equation |An equation that when in standard form is in ax² + | |

| |bx + c = 0 form. | |

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|Solutions |Where the graph of the quadratic function crosses the x-axis. | |

|(also called roots, zeros, or |You can have 0, 1, or 2. | |

|x-intercepts) | | |

EXAMPLE 1 Solve: (2n – 4)(3n + 5) = 0

EXAMPLE 2 What are the roots of the quadratic equation [pic]?

EXAMPLE 3 What are the x-intercepts of the graph of [pic]?

EXAMPLE 4 For what values of x will y = 0 if [pic]?

Example 5 Solve: [pic]

Name______________________DATE___________________PER____________ A 1-2

SOLVING QUADRATIC EQUATIONS

Solve each of the following quadratic equations. Write your solutions in the blank provided to the left of each problem. Work must be shown in order to receive credit!

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|Roots: |(x + 5)(x - 7)=y |

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|Solutions: |2) [pic] |

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|Roots: |3) [pic] |

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|Solutions: |4) [pic] |

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|x-intercepts: |5) [pic] |

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REVIEW 1-3 SOLVING INEQUALITIES

1) Solve and graph the following inequality:

2x – 3 < 7 + 3x

2) Solve and graph the following inequality:

2(4 – d) – 5d > 8

3 Solve and graph the following inequality:

4a + 6 [pic] 7 + 4a

4 Solve and graph the following inequality:

3a – 1 [pic] 3(a + 1)

NAME_________________________DATE_____________PER_______

Solve and graph each of the following. Work must be shown to receive credit.

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|1. Solution: |3x – 7 [pic] 29 |

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|Graph: | |

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|2. Solution: |[pic] + 3 > 9 |

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|Graph: | |

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|3. Solution: |2x – 5(x + 3) [pic] -20 |

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|Graph: | |

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|4. Solution: |4(p – 3) < 4(p – 4) |

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|Graph: | |

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|5. Solution: |12 – 5x [pic] 9x + 8 |

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|Graph: | |

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|6. Solution: |4(2x – 2) [pic] 2(x + 5) |

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|Graph: | |

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|7. Solution: |3r + 1 > 2(r – 6) |

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|Graph: | |

Review 1-4: WRITING THE EQUATION OF A LINE

EXAMPLES: Write the equation of each line in slope-intercept

form.

1) slope of 2 and y-intercept of 15

2) slope of [pic] and y-intercept of -7

It’s “gonna” get harder, right???

A little, but it’s not TOO BAD.

EXAMPLES: Write the equation of each line in slope-intercept

form.

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|3) slope of 1 and goes through |4) slope of [pic] and goes |

|the point (2, 5) |through the point (3, -6) |

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|5) slope of [pic] and y-intercept of |6) slope of -3 and x-intercept of |

|-6 |-3 |

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|Slope of 0 and passes through the point (-3, -5) |

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|NAME___________________________________DATE_________________PER._________ |

|WRITING THE EQUATIONS OF LINES |

|Write the equation of each line described in slope-intercept form. |

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|1. _________________________ |

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|Slope of 2 and y-intercept of 5 |

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|2. _________________________ |

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|Slope of [pic] and x-intercept of 4 |

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|3. _________________________ |

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|Slope of -3 and x-intercept of 3 |

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|4. _________________________ |

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|Slope of 2 and passes through (-5, 1) |

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|5. _________________________ |

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|Slope of 3 and passes through (4, 1) |

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|6. _________________________ |

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|Slope of -2 and passes through (3, 5) |

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|7. _________________________ |

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|Slope of [pic] and passes through (6, -1) |

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Review 1-5: RATIOS & PROPORTIONS

Ratio:

Proportion:

If [pic], then _________________.

EXAMPLES: Determine whether each pair of ratios forms a

proportion.

1. [pic] 2. [pic]

EXAMPLES: Solve each proportion.

3. [pic] 4. [pic]

EXAMPLES: For each word problem, set up a proportion and

solve.

5. In a recent survey, two out of 3 dentists chose Cavity toothpaste for

their patients. If 12 dentists chose Cavity, how many were

surveyed?

6. Hershey Foods makes a batch of chocolate with 75 lbs. of cocoa

beans. If we know that the ratio of cocoa beans to milk is 5: 4, how

many gallons of milk will they use?

7. In the movie Jurassic Park, the dinosaurs were scale models and

so was the sport utility vehicle that the T-Rex overturned. The

vehicle was made to the scale of 1 inch to 8 inches. The actual

vehicle was about 14 feet long. What was the length of the model

sport utility vehicle?

NAME______________________________DATE______________PER.______

RATIOS & PROPORTIONS

Use cross products to determine whether each pair of ratios forms a proportion. SHOW WORK!

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|1. YES or NO |[pic] |

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|2. YES or NO |[pic] |

Solve each proportion. SHOW WORK!

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|3. ____________ |[pic] |

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|4. ____________ |[pic] |

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|5. ____________ |[pic] |

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|6. ____________ |[pic] |

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|7. ____________ |[pic] |

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|8. ____________ |[pic] |

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For each word problem, write a proportion and solve for the indicated value.

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|9. ____________ |Two out of every 3 students in Mr. Pearson’s ninth grade class recycle aluminum cans. If 48 students recycle |

| |aluminum cans, how many students are in Mr. Pearson’s class? |

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|10. ____________ |Cindy’s job is to check computer printers for defects. Out of 420 printers she has to check, only 3 of the |

| |first 84 have been defective. Using this information, what is the best prediction of the total number of |

| |printers in this group that will be defective? |

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|11. ____________ |A recipe for 2[pic] dozen whole-wheat muffins requires 600 g of flour. How many muffins can be made with 900 g|

| |of flour? |

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|12. ____________ |A model airplane is made to the scale 1 inch to 24 inches. If the wing of the actual plane is 18 feet long, |

| |how long will the model wing be? |

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A#1-1

A#1-3

[pic]

[pic]

[pic]

To write the equation of a line when you DON’T have the slope and y-intercept:

1) You must have a point on the line.

2) You must have the slope of the line.

3) Substitute into the point-slope formula:

[pic]

4) Solve for ‘y’ (put in y = mx + b form).

y-coordinate of

given point

x-coordinate of

given point

slope of

line

A#1-4

[pic]

[pic]

[pic]

A# 1-5

A# 1-5; Pg. 2

[pic]

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