Solving one step equations

Solving one step equations lesson and review for chapter 9 & 10 Test

Addition and subtraction to solve one-step equations

• The additive inverse is used when we solve equations that have one step.

• The additive inverse is the opposite signed integer.

• Ex. 3 has the additive inverse of -3

Multiple Choice

What does the absolute value symbol look like?

Multiple Choice

What is the additive inverse of -77?

• 77

• -77

Multiple Choice

What is the additive inverse of 87?

• -87

• 87

Multiple Choice

What is the absolute value of 87?

• -87

• 87

Solving the equation

• Solve: x + 14 = 4

• The inverse of 14 is -14. We subtract -14 from both sides of the equation to solve for x.

• The reason it is done to both sides of the equation is because this is an equality.

• When -14 is added to 14 they cancel but adding -14 to 4 will give a -10 as the answer and the solution as to what x is. The goal is to isolate the variable or get it by itself.

Multiplication and division in one-step equations

• The multiplicative inverse is the reciprocal for the value. Ex. 3 has the reciprocal of

   $\frac{1}{3}$  .

• When solving an equation the idea again is to isolate the variable by using the multiplicative inverse.

• 
  

• 
  

Solve: -5x = 25

• 
  

   $\left(-\frac{1}{5}\right)\ -5x\ =\ 25\ \left(-\frac{1}{5}\right)$  

• x= -5

• Remember your integer rules when solving the equations.

Multiple Choice

Solve for x:

• x = 20
• x = 7
• x = 10
• x = 3

Multiple Choice

Solve the equation:
-5x = 25

• x = 20
• x = -20
• x = -5
• x = 5

Multiple Choice

The multiplicative inverse is the same as the reciprocal.

• true

• false

Multiple Choice

 $\frac{1}{4}\ =\ 8\ \cdot\ m$  

•  $m\ =\frac{1}{4}$  

•  $m\ =\ 2$  

•  $m\ =\ 32$  

•  $m\ =\ \frac{1}{32}$  

Multiple Choice

What is the inverse operation needed to solve the following one-step equation?
100z = 50

• subtraction
• addition
• multiplication
• division

Multiple Choice

What is the inverse operation needed to solve the following one-step equation?
5y = -15

• subtraction
• addition
• multiplication
• division

Multiple Choice

What is the inverse operation needed to solve the following one-step equation?
y / 7 = 14

• subtraction
• addition
• multiplication
• division

Review chapter 9 & 10

• This test will have vocabulary as well as problem solving.

• You will need to go to course documents the day of the test and go into the zoom meeting. The camera and the microphone need to be on during the test. You will then open the test and take it keeping in mind that the mic and camera need to be on the entire test. If they are not on, you will fail the test.

Multiple Choice

Solve the equation shown for k:

• k = 152
• k = 176
• k = 5
• k = 27

Multiple Choice

Solve for y
-4y = 48

• x = -52
• x = -12
• x = -44
• x = -13

Multiple Choice

Solve for x
x - 4 = -3

• x = -7
• x = 1
• x = 12
• x = -12

Multiple Choice

Solve for h
71 + h = -90

• 19
• -19
• -161
• 161

Multiple Choice

Solve for z
z + (-19) = 6

• -13
• 25
• 13
• -25

Multiple Choice

Solve:
(6 x 10⁶) / (2 x 10³)

• 12 x 10³
• 3 x 10⁹
• 1.2 x 10⁴
• 3 x 10³

Multiple Choice

Solve:
(2.1×10​²​​) × (3.0×10​⁴)

• 5.1 x 10²
• 6.3 x 10⁶
• 5.1 x 10⁶
• 6.3 x 10⁸

Multiple Choice

Write the answer in scientific notation.
4.1 x 10⁵ +   5.5 x 10⁶  =

• 5.91 x 10⁶
• 9.6 x 10⁵
• 9.6 x 10¹¹
• 4.65 x 10⁵

Multiple Choice

Write the answer in scientific notation.
7.3 x 10⁵  +   3.7 x 10⁵  =

• 11.0 x 10⁵
• 1.1 x 10¹⁰
• 1.10 x 10¹¹
• 1.1 x 10 ⁶

Multiple Choice

How would you write 0.0005 in scientific notation?

• 50 x 10⁵
• 5 x 10⁴
• 5 x 10³
• .5 x 10³

Multiple Choice

How would you write 564,000,000 in scientific notation?

• 5.64 x 10^-7
• 5.64 x 10⁶
• 5.64 x 10⁸
• 56.4 x 10⁷

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

According to exponent rules, when we multiply the coefficients we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

According to exponent rules, when we divide the coefficients we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

w⁵/w⁸

• w³
• 1/w³
• w¹³
• w⁴⁰

Multiple Choice

(-7)⁰⋅g

• -7g
• g
• 0
• -7

Multiple Choice

5c²⋅(2c³)⁴

• 80c⁹
• 10c¹⁴
• 10c²⁴
• 80c¹⁴

Multiple Choice

(X²Y⁷/X³Y⁵)⁰

• 0
• Y²/X
• 1
• XY

Multiple Choice

11⁸/11³

• 11¹¹
• 11⁵
• 11²⁴
• 1⁵

Multiple Choice

5^-2

• -25
• -10
• -1/25
• 1/25

Multiple Choice

(m²)⁵

• m⁷
• m²⁵
• m³
• m¹⁰

Multiple Choice

x³(x⁹)

• x³
• x²⁷
• x¹²
• x⁶

Multiple Choice

-15 - 3

• 12
• -12
• -18
• 18

Multiple Choice

44/-4=

• 11
• -8
• -11
• -1/11

Multiple Choice

Is the product
–8 • (–3) positive or negative?

• negative
• positive
• both
• neither

Multiple Choice

The record high January temperature for Houston, Texas is 88⁰ F. The record low January temperature is -5⁰ F. Find the difference between the high and low temperatures.

• -83⁰
• 83⁰
• -93⁰
• 93⁰

Multiple Choice

-3(-4)

• -12
• 7 
• -7
• 12

Multiple Choice

(-25) ÷ (-5)

• 5
• -5
• -20
• -30

Multiple Choice

-4(5)

• -20
• 1
• 20
• -1

Multiple Choice

3 + -7

• 10
• 4
• -10
• -4

Multiple Choice

-9 + (-5)

• -14
• 14
• -4
• 4

Multiple Choice

Express an integer: a debt of $50

• 50
• -50
• +50

Multiple Choice

Solve -13 + I -5 I 

• 8
• -8
• -18
• 18

Multiple Choice

The sea turtle swims 28 feet below sea level.  Which integer best represents this distance?

• -28 feet
• 28 feet
• 28 - 0 feet
• ∣-28∣

Multiple Choice

Solve the following:
-13 + 173 = ?

• 186
• -186
• 160
• -160

Multiple Choice

What is the opposite of -237?

• zero
• 237

Multiple Choice

Zero...

• has an absolute value of zero

• is its own opposite

• is not positive or negative

• all of the above are correct

Multiple Choice

Put the following numbers in order from greatest to least: -8,|-9|, 5, 0, |7|, -2

• |-9|, -8, -2, 0, 5, |7|

• -2, -8 , 0, 5, |7|, |-9|

• |-9|, |7|, 5, 0 -2, -8

• |-9|, |7|, -8, 5, -2, 0

Multiple Choice

Which has a larger absolute value, -4 or 3?

• -4

• 3

Multiple Select

Choose ALL correct statements about the integers -7 and 7.

• they are opposites

• they are equal

• they have nothing in common

• they have the same absolute value

Multiple Choice

Which set of numbers is in order from least to greatest?

• 17, 10, 8, 6, 2, -4, -9

• -9, -4, 2, 6, 8, 10, 17

• neither

• both

Multiple Choice

-8 ____ -9

• <

• >

• =

Multiple Choice

In 2x + 5 = 11, the 5 is called:

• A variable
• A constant
• A coefficient

Multiple Choice

In 6xy + 7z + 4, the 6xy is called:

• A coefficient
• A term
• A constant
• A variable

Multiple Choice

A term that does not contain a variable is called:

• a coefficient
• a constant
• a term
• an expression

Multiple Choice

The numerical factor of a term that contains a variable is called: 

• a constant
• a coefficient
• a term
• a variable

Multiple Choice

A placeholder or letter used to represent an unspecified value is called:

• a variable
• a coefficient
• a constant
• a term

Multiple Choice

2b - 5 is called:

• an equation
• an algebraic expression
• a term
• an inequality

Multiple Choice

The x in 7x is called:

• a term
• a variable
• a coefficient
• a constant

Multiple Choice

7 + 3 = 10 is called:

• An algebraic expression
• An equation
• An inequality

Multiple Choice

A number, variable, or the product of numbers and/or variables is called:

• an equation
• an algebraic expression
• a term
• a coefficient

The test will begin at 10:15 a.m. Make sure you have your note cards ready. You will have one hour to finish the test. Study and I will see you next class.

Multiple Choice

What is the value of V?

V + 23 = 45

• V = 68

• V = 22

• V = -22

• Not Here

Multiple Choice

Evaluate (solve).

y - 4.6 = 12

• y = 16.6

• y = 5.8

• y = 7.4

• Answer not Given

Multiple Choice

Solve for x.

x + 12 = 20

• x = 8

• x = -32

• x = 32

• x = -8

Multiple Choice

x - 62 = 123
How should you show your work to isolate the variable and solve the equation?

• Subtract 62 from each side. 
• Add 62 to each side.
• Multiply each side by 62.
• Add 123 to each side.

Multiple Choice

Evaluate (Solve):

f-22=36

• f = 62

• f = 14

• f = 58

• f = 12

Multiple Choice

What is the correct step to solve for the variable?
15 = m - 5

• add 5 to both sides
• add 15 to both sides
• subtract 15 from both sides
• subtract 5 from both sides

Multiple Choice

The inverse operation of addition is _______________.

• Division
• Multiplication
• Addition
• Subtraction

Multiple Choice

To solve one-step equations, you have to use the ________________ operation.

• Integer
• Inverse
• Additive
• Subtractive

Multiple Choice

In an equation, you want to get the variable...

• on one side
• to disappear
• by itself
• to sing and dance

Multiple Choice

When you solve one-step equations, you can do anything you want to one side of the equal sign, as long as...

• it is mathematical
• you do the SAME thing to the other side
• solving equations is impossible
• I love Snow Days!

Multiple Select

What are the two basic rules for solving algebraic equations?

• Whatever you do to one side of the equal sign, you must copy and do on the other side of the equal sign

• Negative signs can be ignored

• Always start on the left side, regardless of where the variable is

• Always do the opposite operation