Lesson on Solving Equations

Solving Equations

by Aqil Mohammed

​Solving One-Step Equations

​

​Solving Two-Step Equations

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Solving Equations with Variables on Each Side

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Solving Multi-Step Equations

Solving Equations with Variables on Each Side

Learning Objectives:

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​-

​ALEF LESSONS 35 & 36

​Learning Objectives:

​

​- How to solve one-step equations with fraction coefficients

​

​- How to solve one-step equations with decimal coefficients

Starter:​

Answer the following five questions!​

Multiple Choice

6 + [ ] = 12

• 6

• 4

• 2

• 10

Multiple Choice

5 + [ ] = 14

• 10

• 3

• 9

• 6

Multiple Choice

15 - ___ = 8

• 6

• 3

• 7

• 5

Multiple Choice

__ - 4 = 8

• 12

• 18

• 4

• 6

Multiple Choice

__ + 7 = 14

• 4

• 12

• 7

• 3

Solving one-step equations

​To solve one-step equations, we need to get the unknown variable on its own.

​

On the right are some examples of one-step equations.​

​

​Easy way to remember the method is

'To find the unknown, we need to make it alone.'

​

Example 1

​The unknown variable here is x, we want to make x alone.

​

​So, since we are adding 2 to x, we need to think about the inverse operation.

​

​The inverse of addition is subtraction, so we subtract 2 from both sides.

Multiple Choice

In the equation x + 7 = 12, 7 is being added to the variable, x. How should you show your work to isolate the variable and solve the equation? 

• Subtract 7 from both sides. The solution is x = 5.
• Add 7 to both sides.
  The solution is x = 19.
• Multiply both sides by 7. The solution is x = 84.

Example 2

​The unknown variable here is y, we want to make y alone.

​

​Since we are subtracting 4 from y, we need to think about the inverse operation.

​

​The inverse of subtraction is addition, so we add 4 to both sides.

Multiple Choice

x - 62 = 123

What step would you have to take to solve the equation?

• Add 62 to each side.

  x = 185

• Subtract 62 from each side.

  x = 61

• Multiply each side by 62.

  x = 7626

• Add 123 to each side.

  x = 246

Example 3

​The unknown variable here is a, we want to make a alone.

​

​Since we are multiplying a by 3, we need to think about the inverse operation.

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​The inverse of multiplication is division, so we divide both sides by 3.

Multiple Choice

What step would you have to take to solve the following equation?

9x = 153

• multiply by 9 on both sides

  x = 1377

• divide by 9 on both sides

  x = 17

• add 9 to both sides

  x = 162

• subtract 9 from both sides

  x = 144

Example 4

​The unknown variable here is b, we want to make b alone.

​

​Since we are dividing b by 2, we need to think about the inverse operation.

​

​The inverse of division is multiplication, so we multiply both sides by 2.

Multiple Choice

What step would you have to take to solve the following equation?

$$\frac{x}{3}\ =\ 6$$  

• multiply by 3 on both sides

  x = 18

• divide by 3 on both sides

  x = 2

• add 3 to both sides

  x = 9

• subtract 3 from both sides

  x = 3

​Now let's look at solving equations where the coefficient is a fraction

Multiple Choice

The following is an example of _____________

7 * (1/7) = 1

• Multiplicative Identity
• Commutative Property
• Multiplication Property of Equality
• Multiplicative Inverse

Multiple Choice

What is the multiplicative inverse of 12/7?

• 7/12
• 1  5/7
• 3/6
• 12/7

Multiple Choice

What is the multiplicative inverse of 2/3?

• 2/3
• 1/4
• 3/2
• 4/6

Multiple Choice

What is the multiplicative inverse of 7/8?

• 1
• 14/16
• 8/7
• 7/8

Multiple Choice

What is the multiplicative inverse of -3/4?

• 1
• -6/12

• -4/3

• 4/3

Let's practice​!

Multiple Choice

Solve for x:

$$\frac{1}{5}x\ =\ 2$$  

• x = 20
• x = 7
• x = 10
• x = 3

Multiple Choice

Solve the equation. Check your solution.

$$6\ =\ \frac{1}{12}v$$  

• 72
• .5
• ¹/₂
• 2

Multiple Choice

$$\frac{1}{3}x=-12$$  

• x = -4

• x = -36

• x = 4

• x = 36

Multiple Choice

Solve the equation.

$$\frac{5}{6}m\ =\ 20$$  

• 6

• 10

• 12

• 24

Multiple Choice

Solve the equation. Check your solution.

$$-\frac{2}{3}w\ =\ 60$$  

• -90
• 90
• -40
• -180

Multiple Choice

Change to an improper fraction

• 24/5

• 10/5

• 30/5

• 34/5

Multiple Choice

Change to an improper fraction

• 5/22

• 12/2

• 4/12

• 12/5

Multiple Choice

8/5= what as a mixed number?

• 1  2/5
• 1  4/5
• 1  1/5
• 1  3/5

Multiple Choice

32/10=what as a mixed number?

• 3 1/5

• 2 2/10

• 3/10

• 3 1/10

Multiple Choice

Solve for w:

$$\frac{3}{2}w\ =\ 12$$  

• w = 18

• w = 8

• w = 11

• w =

Multiple Choice

Solve for a:

$$2\ \frac{1}{3}a\ =\ 14$$  

• a = 4

• a = 2

• a = 6

• a = 21

​Go to ALEF Lesson 35

-Complete Check You​r Understanding 1

​

​

-Complete Exit Ticket​

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​Now let's look at solving equations where the coefficient is a decimal

Multiple Choice

1.25 = 2.5b

• 1.2

• 2

• 0.5

• 1.5

Multiple Choice

3.6k = 7.56

• 2.8

• 3.96

• 0.48

• 2.1

Multiple Choice

1.2h = 10.8

• 0.11

• 8

• 9

• 10

Multiple Choice

Solve the equation. Check your answer.
-2.5b = 20.5 

• 8.2
• -0.12
• 0.12
• -8.2

ALEF Lesson 36 Relate Activity​

Now we're going to learn how to write​ and solve equations to solve real-world problems.

Poll

Rate your Understanding of this topic

• Fantastic!

• Okay

• I need help!

​Go to ALEF Lesson 36

• Complete Check You​r Understanding 2

​

• ​Complete Check Your Understanding 3

​

• Complete Exit Ticket​

​

​ALEF LESSONS 37 & 38

​Learning Objectives:

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​- How to identify and solve two-step equations

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​- How to solve two-step equations in a variety of situations

​

Starter:​

Answer the following 4 questions!​

Multiple Choice

Solve the equation:
20.5 = x + 4

• 16.5
• 16.05
• 24.5
• 24.05

Multiple Choice

y - 33 = 147

• y = 114
• y = 177
• y = 180
• Answer not Given

Multiple Choice

Solve the equation
3x = 27. 

• x = 24
• x = 81
• x = 9

Multiple Choice

Solve the following equation
c / 4 = 4

• 1/4
• 8
• 1
• 16

Let's Practice!​

Multiple Choice

$$14x-10=4$$  

• $$x=-8$$  

• $$x=10$$  

• $$x=1$$  

• $$x=-14$$  

Multiple Choice

$$-4x+3=-29$$  

• $$x=4$$  

• $$x=6$$  

• $$x=2$$  

• $$x=8$$  

Multiple Choice

$$\frac{x}{-11}+8=6$$  

• $$x=-22$$  

• $$x=1$$  

• $$x=11$$  

• $$x=22$$  

Multiple Choice

$$-5x-1=-16$$  

• $$x=3$$  

• $$x=-4$$  

• $$x=2$$  

• $$x=5$$  

Multiple Choice

$$\frac{x}{1}+3=33$$  

• $$x=9$$  

• $$x=10$$  

• $$x=-11$$  

• $$x=30$$  

​Go to ALEF Lessons 37 and 38

• Complete Check You​r Understanding 1

​

• ​Complete Check Your Understanding 2

​

• Complete Exit Ticket​s

​

Poll

Rate your Understanding of this topic

• Fantastic!

• Okay

• I need help!