Solving for a Variable Two Step Problems

Mrs. Higgins won a certain number of jolly ranchers playing the football toss at the Fall Festival.  At school she gave 21 away to her students. She only has 5 remaining. How many did she win total to be able to give away? Write an equation to solve this problem using g as your variable.

• g/21=5

• g-21=5

• g-5=21

• g+5=21

To isolate x if ax=b, you should...

• Multiply both sides by a.

• Subtract a from both sides.

• Divide both sides by b.

• Divide both sides by a.  

After paying $3.32 for a sandwich, Mr. Thrasher has $19.79. How much money did he start with? Which equation could you use to solve this problem?

• 3.32m=19.79

• m-19.97=3.32

• m-3.32=19.79

Simply and solve.
8y  +  2y  - 4y  =  126

• y= 120

• y = -1

• y= 21

• y = 131

Simplify and solve.
a  + 3a  - 2a   + 7a  =  -72

• a= -6

• a= 9

• a= -4

• a= -8

Mrs. Brown,the librarian, bought three new books for a total of $18.00. If each book cost the same amount, how much did each book cost? Write an equation to solve this problem. Use c as your variable.

• 18c=6

• c + 6= 18

• c +18 = 6

• 3c=18

Why do we use inverse operations when solving two step equations?

• To isolate the variable

• To simplify the constants

• To make the equation more complex

• To add more steps to the solution

Answer explanation

The goal in solving an equation is to get the variable alone on one side of the equation and a number on the other side of the equation. In order to do this we must isolate the variable by reversing the operations acting on the variable. For example if we have 4x the inverse operation of multiplication is division so we would divide 4x by 4

Solve the equation 2x + 8 =18. What is x?

• 7

• 6

• 8

• 5

Answer explanation

To solve the equation 2x + 8 = 18, first subtract 8 from both sides to get 2x = 10. Then divide by 2 to find x = 5. Therefore, x = 5 is the correct answer.

Which of the following solutions is correct for the equation 4x+6=18?

• x=1

• x=4

• x=3

• x=2

Answer explanation

To solve the equation 4x+6=18, first subtract 6 from both sides to get 4x=12. Then divide by 4 to find x=3. Therefore, the correct solution is x=3.

If you were to create a two step equation where the value of x =4 what would the equation look like?

• 2x+4=11

• 2x+3=11

• 3x+2=11

• 3x+3=11

Answer explanation

The correct equation for x=4 would be 2x+3=11. Plugging in x=4 gives 2(4)+3=11, which simplifies to 8+3=11.