2-1 Writing and Interpreting Equations

2-1 Writing and Interpreting Equations

​Learning Goal:

• ​I can write and interpret equations.​

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​What is an equation?

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An equation is a mathematical sentence that says two expressions are equal. It has to have an equal sign (=)

​Notes - Example 1

​Write an equation for the sentence.

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​The quotient of 24 and x equals 14 minus 2 times x

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​Try it on your own and then move ahead to see the answer :)

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​Notes - Example 1

​Write an equation for the sentence.

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​The quotient of 24 and x equals 14 minus 2 times x

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​

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​The next slide will check to see if you've got it :)

Multiple Choice

Write an equation for the sentence.

Ten minus four times a number is equal to 16.

• 4x - 10 = 16

• 4(x - 10) = 16

• 10 - 4x = 16

• 4x + 10 = 16

​Example 2

​Nine times a number y subtracted from 85 is seven times the sum of four and y

​

​Try this one on your own :)

​Example 2

​Nine times a number y subtracted from 85 is seven times the sum of four and y

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​85 - 9y = 7(4 + y)

​Question 3

​ATHLETICS: Of 107 athletes surveyed about what sport they play, some play basketball. Of those that play basketball, 48 play baseball and the remaining 33 do not play baseball. Write an equation to find the number of athletes surveyed who do not play basketball.

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​Question 3

​ATHLETICS: Of 107 athletes surveyed about what sport they play, some play basketball. Of those that play basketball, 48 play baseball and the remaining 33 do not play baseball. Write an equation to find the number of athletes surveyed who do not play basketball.

​

What equation can we make?

​(We don't actually need to solve,

​just write the equation.)

​Question 3

​ATHLETICS: Of 107 athletes surveyed about what sport they play, some play basketball. Of those that play basketball, 48 play baseball and the remaining 33 do not play baseball. Write an equation to find the number of athletes surveyed who do not play basketball.

​

What equation can we make?

​(We don't actually need to solve,

​just write the equation.)

​Question 3

​ATHLETICS: Of 107 athletes surveyed about what sport they play, some play basketball. Of those that play basketball, 48 play baseball and the remaining 33 do not play baseball. Write an equation to find the number of athletes surveyed who do not play basketball.

​

What equation can we make?

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​48 + 33 + n = 107

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​We can use any letter,

I just picked n

​Question 4

​SALES: Cars and trucks are the most popular vehicles. Last year, the number of cars sold was 39000 more than three times the number of trucks sold. There were 216000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year.

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​Question 4

​SALES: Cars and trucks are the most popular vehicles. Last year, the number of cars sold was 39000 more than three times the number of trucks sold. There were 216000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year.

​Let's use c

for cars

and

t for trucks.

​

​

​

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​Question 4

​SALES: Cars and trucks are the most popular vehicles. Last year, the number of cars sold was 39000 more than three times the number of trucks sold. There were 216000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year.

​Let's use c for cars and t for trucks.

c = 39000 + 3(t) <-------- number of cars is 39000 more than 3 times trucks

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​Question 4

​SALES: Cars and trucks are the most popular vehicles. Last year, the number of cars sold was 39000 more than three times the number of trucks sold. There were 216000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year.

​Let's use c for cars and t for trucks.

c = 39000 + 3(t)<-------- number of cars is 39000 more than 3 times trucks

​We know c = 216000, so we can plug it in to the equation above.

​

​

​Question 4

​SALES: Cars and trucks are the most popular vehicles. Last year, the number of cars sold was 39000 more than three times the number of trucks sold. There were 216000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year.

​Let's use c for cars and t for trucks.

c = 39000 + 3(t)<-------- number of cars is 39000 more than 3 times trucks

​We know c = 216000, so we can plug it in to the equation above.

​216000 = 39000 + 3(t) <----------------This is our equation we can use.

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​Question 5

​The sum of x and its square is equal to y times z.

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​Try this one first and then move ahead to see the answer! :)

​Question 5

​The sum of x and its square is equal to y times z.

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​( x + x²) = y(z)

​Question 6

​Four times the sum of f and g is identical to six times g

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​Try this one first and then check your answer!

​Question 6

​Four times the sum of f and g is identical to six times g

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​4(f + g) = 6g

​Question 7

Write a sentence for the equation.​

g+20=3g

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​The sum of g and 20 is equal to the product of 3 and g.

​Question 8

​Write a sentence for the equation.

7p+23=102

7 times p plus 23 equals 102​

​Now we will be starting lesson 2-2.

​Start a new page of notes for this lesson so you don't get them mixed up!

2-2 Solving One-Step Equations​

​Notes - Addition and Subtraction

​Addition Property of Equality - we can add a number to both sides of an equation. We can use this to solve an equation that has subtraction.

​If a = b, then a + c = b + c

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Subtraction Property of Equality - we can subtract a number from both sides of an equation. We can use this to solve an equation that has addition.

​If a = b, then a - c = b - c

​Notes - Example 1

​Solve using the Addition Property of Equality

​

​g - 25 = 113

g - 25​ + 25 = 113 + 25

g = 138​

​Add 25 to both sides.

​Simplify both sides.

​(Remember -25 and +25 cancel each other.)

Fill in the Blanks

Solve for x using the Addition Property of Equality.

x - 45 = 50

​Notes - Example 2

​Solve using the Subtraction Property of Equality.

​27 + k = 30

​27 + k - 27 = 30 - 27

​k = 3

​Subtract 27 from both sides.

​Simplify both sides.

​(Remember, 27 - 27 = 0 and 30 - 27 = 3)

Fill in the Blanks

Solve for y using the Subtraction Property of Equality.

y + 20 = 87

​Notes - Multiplication and Division

​Notes - Example 3

​Multiply both sides by 3 so 1/3 will cancel.

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​Simplify both sides. (Remember that 1/3 times 3 equals 1.)

Fill in the Blanks

Solve for x using the Multiplication Property of Equality.

$\frac{a}{6}=-9$  

​Notes - Example 4

​​Solve the equation.

​

​

​Since we want to solve for y, we can divide by -14 so -14y becomes y.

​We have to divide the other side by -14 too, so 42 / -14 = -3.

​The answer is y = -3

Fill in the Blanks

Solve for w using the Division Property of Equality.

12t = -132

​Homework:

• ​Paper: 2-1 Practice, 2-1 Homework, 2-2 Practice, 2-2 Homework

• Online: 2-1 and 2-2 (McGraw Hill, Period # Algebra 1)

• The papers are due today, and the online is due Wednesday.