Multi-Step Equation Solving including Special Cases

What would be the best first step to solve this equation:

 $12-2p=17$  

• Divide by 2 on both sides

• Add 12 to both sides

• Add 2 to both sides

• Subtract 12 from both sides

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

What would be the best next step to solve this equation:

 $3-5c=8+2c$  

• Add 5c to both sides

• Add 8 to both sides

• Add 3 to both sides

• Subtract 5c from both sides

Tags

CCSS.HSA.REI.B.3

Solve:

 $7x-3x-8=24$  

•  $x=8$  

•  $x=3.2$  

•  $x=-8$  

•  $x=4$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve:

 $6\left(5x-3\right)+2=14$  

•  $x=2$  

•  $x=-1$  

•  $x=0.5$  

•  $x=1$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

James solves the above equation and gets 5 = -3. What is the solution to this equation?

• infinite solutions

• no solution

• x = 5

• x = -3

• none of these

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve:

 $3x+15=3\left(x+5\right)$  

• No solution

• Infinitely many solutions

•  $x\ =\ 15$  

• none of these

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Without solving, state whether the equation has one, no or infinite solutions:

 $5x+6=2+3x$  

• one

• no solution

• infinite solutions

Tags

CCSS.HSA.REI.B.3

Karl solved an equation for x and found 3 = 3.

Which statement best describes the solution to the equation that Karl was solving?

•  $x=3$  

• There is no solution

• There are infinite solutions

Carlos solved the equation and got x = -5.

When he substituted his answer back into the equation to check his work, he got -10 = -22 and realized he had made a mistake.

Where is his mistake?

• -2 - 3 = -1 , so x = -1

• Distribute the 5 to the 3 to get 15 instead of 3

• Subtract 5x from each side

• Add 2 to each side

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve:
 $3x-4=2x+8$  

Enter only the value of x, not "x = ___".  No spaces.  If no solution, enter "no solution" -- if infinite solutions, enter "infinite solution".

Tags

CCSS.HSA.REI.B.3