Understanding How to Solve Simple Equations (Grade 9)

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Understanding How to Solve Simple Equations

1. 
The first step of solving an equation is given. Choose the correct justification for this first step.

[math] 3x+2 [/math][math]= \ \ 10[/math]
[math]3x+2-2[/math][math]= \ \ 10-2 [/math]
  1. Addition Property of Equality
  2. Subtraction Property of Equality
  3. Multiplication Property of Equality
  4. Division Property of Equality
2. 
The first step of solving an equation is given. Choose the correct justification for this first step.

[math] 3(x-9) [/math][math]= \ \ 16[/math]
[math](3(x-9))/3[/math][math]= \ \ 16/3 [/math]
  1. Addition Property of Equality
  2. Subtraction Property of Equality
  3. Multiplication Property of Equality
  4. Division Property of Equality
3. 
The first step of solving an equation is given. Choose the correct justification for this first step.

[math] 5/2 x + 4 [/math][math]= \ \ \ \ 8[/math]
[math]2(5/2 x + 4)[/math][math]= \ \ 2(8) [/math]
  1. Addition Property of Equality
  2. Subtraction Property of Equality
  3. Multiplication Property of Equality
  4. Division Property of Equality
4. 
The first step of solving an equation is given. Choose the correct justification for this first step.

[math] 4x-5 [/math][math]= \ \ -3[/math]
[math]4x-5+5[/math][math]= \ \ -3+5 [/math]
  1. Addition Property of Equality
  2. Subtraction Property of Equality
  3. Multiplication Property of Equality
  4. Division Property of Equality
5. 
A solution to the equation is given, except for one step. Choose the correct action for the missing step.

[math]3x+6 = 9[/math]

Step 1:[math] 3x+6-6 [/math][math]= \ \ 9-6[/math]
Step 2:[math]3x[/math][math]= \ \ 3 [/math]
Step 3:[math] \ \ [/math][math] \ \ [/math]
Step 4:[math]x[/math][math]= \ \ 1 [/math]
  1. Add 3 to both sides.
  2. Divide both sides by 3.
  3. Subtract 3 from both sides.
  4. Take the cube root of each side.
6. 
A solution to the equation is given, except for one step. Choose the correct action for the missing step.

[math]3x+5 = x-1[/math]

Step 1:[math] \ \ \ [/math][math] \ \ \ [/math]
Step 2:[math] 3x [/math][math]= \ \ x- 6[/math]
Step 3:[math]3x-x[/math][math]= \ \ x-6-x [/math]
Step 4:[math]2x[/math][math]= \ \ -6 [/math]
Step 5:[math](2x)/2[/math][math]= \ \ (-6)/2 [/math]
Step 6:[math]x[/math][math]= \ \ -3 [/math]
  1. Subtract 6 from the right hand side.
  2. Remove 5 from the left hand side.
  3. Add 5 to both sides.
  4. Subtract 5 from both sides.
7. 
A solution to the equation is given, except for one step. Choose the correct action for the missing step.

[math]2x + 3 = 4x[/math]


Step 1:[math] \ \ \ [/math][math] \ \ \ [/math]
Step 2:[math]3[/math][math]= \ \ 2x [/math]
Step 3:[math] 3/2 [/math][math]= \ \ (2x)/2 [/math]
Step 4:[math]3/2[/math][math]= \ \ x [/math]
  1. Subtract 3 from both sides.
  2. Add 3 to both sides.
  3. Subtract 2x from both sides.
  4. Divide by 2x on both sides.
8. 
A solution to the equation is given, except for one step. Choose the correct action for the missing step.

[math](3x)/2 + 4 = 4/5[/math]

Step 1:[math] (3x)/2 + 4 - 4 [/math][math]= \ \ 4/5 - 4[/math]
Step 2:[math](3x)/2[/math][math]= \ \ -16/5 [/math]
Step 3:[math] \ \ \ [/math][math] \ \ \ \ [/math]
Step 4:[math]3x[/math][math]= \ \ -32/5 [/math]
Step 5:[math](3x)/3[/math][math]= \ \ -32/(5*3) [/math]
Step 6:[math]x[/math][math]= \ \ -32/15 [/math]
  1. Multiply by 2 on both sides.
  2. Get rid of the fraction on the left hand side.
  3. Multiply by 1/2 on both sides.
  4. Subtract 16/5 from the left hand side.
9. 
Is the solution to the equation correct? If not, identify which step contains an error and why this step is incorrect.

[math] 5x - 7 = 8[/math]

Step 1:[math] 5x-7+7 [/math][math]= \ \ 8[/math]
Step 2:[math]5x[/math][math]= \ \ 8 [/math]
Step 3:[math] \(5x)/5 [/math][math]= \ \ 8/5 [/math]
Step 4:[math]x[/math][math]= \ \ 8/5 [/math]
  1. It is correct.
  2. Step 1 is incorrect because you should divide by 5 first.
  3. Step 1 is incorrect because you have to add 7 to both sides.
  4. Step 3 is incorrect because you only need to cancel the 5, not divide.
10. 
Is the solution to the equation correct? If not, identify which step contains an error and why this step is incorrect.

[math] 3x - 2 = 10 - x[/math]

Step 1:[math] 3x-2+x [/math][math]= \ \ 10-x+x[/math]
Step 2:[math]4x-2[/math][math]= \ \ 10 [/math]
Step 3:[math] 4x-2+2 [/math][math]= \ \ 10+2 [/math]
Step 4:[math]4x[/math][math]= \ \ 12 [/math]
Step 5:[math](4x)/4[/math][math]= \ \ 12 [/math]
Step 6:[math]x[/math][math]= \ \ 12 [/math]
  1. It is correct.
  2. Step 1 is incorrect because you have to start with getting rid of the -2.
  3. Step 1 is incorrect because you should divide by 3 on both sides.
  4. Step 5 is incorrect because you have to divide by 4 on both sides.

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