Review of all things equations

Draw

How can you make the equation below true by moving only ONE matchstick?

Multiple Choice

What is the solution to the equations?

• one solution
• no solution
• infinite solutions
• none of these

Match

Match the following

• No Solution

• Infinite Solutions

• One Solution

3x+4=3x-10

4x-x=3x

-2x+4=-2x

• 3x+4=3x-10

• 4x-x=3x

• -2x+4=-2x

Multiple Choice

What is the solution to this equation?

• one solution
• no solution
• infinite solutions
• none of these

Multiple Choice

How many solutions does the equation have?

$$0.9x+5.1x-7=2\left(2.5x-3\right)$$

• no solution

• one solution

• infinite solutions

Multiple Choice

What is the first step?

$$6v+8v+20=118$$  

• Combine like terms

  6v+8v

• -20 from both sides

• -118 from both sides

• +20 to both sides

Multiple Choice

What is the second step step?

$$6v+8v+20=118$$  

$$14v+20=118$$

• -20 from both sides

• -118 from both sides

• +20 to both sides

Multiple Choice

What is the third step step?

$$6v+8v+20=118$$  

$$14v+20=118$$

$$14v=98$$

• multiply by 14 on both sides

• divide by 14 on both sides

• -98 on both sides

Multiple Choice

Solve for v.

$$6v+8v+20=118$$  

• v = 7

• v = 98

• v = 20

• v = 0

Multiple Choice

What is the first step

2x - 12 = -5x +4x

• -2x from both sides

• +5x to both sides

• -4x from both sides

• Combine like terms on the same side

  -5x+4x=-1x

Multiple Choice

What is the second step

2x - 12 = -5x +4x

2x-12=-1x

• Move constants (numbers) to one side

  +12 to both sides

• Move variables (letters) to one side

  +1x to both sides

• Divide both sides by -1

• Divide both sides by 2

Multiple Choice

What is the third step

2x - 12 = -5x +4x

2x-12=-1x

3x-12=0

• Move constants (numbers) to one side

  +12 to both sides

• Move variables (letters) to one side

  -3x to both sides

• Move constants (numbers) to one side

  -12 to both sides

• Divide both sides by 3

Multiple Choice

Solve for x

2x - 12 = -5x +4x

• x = 3

• x = 4

• x = -3

• x = -4

Reorder

Reorder the following steps to solve for x

5(x-4) + 3x -1 = 10x -2

• Combine like terms

• Distribute the 5

• Subtract 8x

• Add 3

• Divide by 2

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

What is the first step

3x + 2(4x - 4) = 3

• -3x from both sides

• multiply the 2 and 4x

• Distribute the 2 and multiply it to all numbers in parenthesis making it 8x-8

• +4 to both sides

Multiple Choice

What is the second step

3x + 2(4x - 4) = 3

3x+8x-8=3

• Combine like terms

  3x+8x=11x

• Combine like terms

  -8+3

• move the constants to one side by +8 to both sides

• move the constants to one side by -8 to both sides

Multiple Choice

What is the second step

3x + 2(4x - 4) = 3

3x+8x-8=3

11x-8=3

• Divide both sides by 11

• Multiply both sides by 11

• +8 to both sides

• -8 to both sides

Multiple Choice

What is the second step

3x + 2(4x - 4) = 3

3x+8x-8=3

11x-8=3

11x=11

• Divide both sides by 11

• Multiply both sides by 11

• +11 to both sides

• -11 to both sides

Multiple Choice

Solve the equations:

3x + 2(4x - 4) = 3

• 4

• 3

• 2

• 1

Reorder

What are the first 3 steps

$$-\frac{3}{5}x-\frac{7}{10}x+\frac{1}{2}x=-56$$

• Find the LCD which is 10

• Multiply everything by 10

  $$10\left(-\frac{3}{5}x-\frac{7}{10}x+\frac{1}{2}x\right)=-56\cdot10$$

• Get your new equation without fractions

  -6x-7x+5x=-56

1

2

3

• 1
• 2
• 3

Multiple Choice

$$-\frac{3}{5}x-\frac{7}{10}x+\frac{1}{2}x=-56$$

$$10\left(-\frac{3}{5}x-\frac{7}{10}x+\frac{1}{2}x\right)=-56\cdot10$$

$$-6x-7x+5x=-56$$

what is the next step

• Combine like terms

  -6x-7x+5x=-8x

• +56 to both sides

• Combine like terms -6x-7x= -13x

• Combine like terms -7x+5x=-2x

Multiple Choice

$$-\frac{3}{5}x-\frac{7}{10}x+\frac{1}{2}x=-56$$

$$10\left(-\frac{3}{5}x-\frac{7}{10}x+\frac{1}{2}x\right)=-56\cdot10$$

$$-6x-7x+5x=-56$$

-8x=-56

what is the next step

• multiply both sides by -8

• Divide both sides by -8

• +8 to both sides

• -8 to both sides

Multiple Choice

$$-\frac{3}{5}x-\frac{7}{10}x+\frac{1}{2}x=-56$$

• x=70

• x= $$-\frac{728}{9}$$

• x=-140

• x=-504/5