Solving Equations

The objective when solving an equation is to....

• isolate the variable.

• check the solution.

• guess and check.

• hope you get the right answer.

Answer explanation

Remember that our goal when we solve an equation for a variable, like b, is to get the variable equal to everything else: b = ___________

Tags

CCSS.7.EE.B.4A

What is the first step to solve this equation?

 $5+6k=-13$  

• Add 13 to both sides

• Subtract 5 from both sides

• Subtract 6 from both sides

• Divide both sides by 6

Answer explanation

The first step is to move the other term away from the variable term.  You are trying to get 6k by itself.  So we have to "undo" the 5.  Since 5 is positive, we undo it by subtracting 5 from both sides of the equation.

Tags

CCSS.7.EE.B.4A

What is the next step to solve this equation?

 $6k=-18$ 

• Add 18 to both sides

• Subtract 18 from both sides

• Subtract 6 from both sides

• Divide both sides by 6

Answer explanation

Now, we have 6k, which is 6 times k, but we only want k.  So we have to "undo" the 6 by doing the opposite operation ... divide both sides of the equation by 6.

Tags

CCSS.6.EE.B.7

Solve:

 $4n-10=62$  

•  $n=-15$  
  

•  $n=18$  

•  $n=12$  
  

•  $n=-8$  

Answer explanation

 $4n-10=62$  

Step 1: add 10 to both sides and simplify
 $4n=72$  

Step 2: divide both sides by 4 and simplify
 $n=18$  

Tags

CCSS.7.EE.B.4A

Solve for x.

 $-23=2-5x$  

•  $x=-14$  

•  $x=-13$  

•  $x=5$  

•  $x=6$  

Answer explanation

 $-23=2-5x$  

Step 1: subtract 2 from both sides and simplify
(don't forget to keep the negative sign with the 5x)
 $-25=-5x$  

Step 2: divide both sides by -5 and simplify
 $5=x$  

Tags

CCSS.7.EE.B.4A

What is the first step to solve this equation?

 $2=\frac{n}{5}$  

• subtract 2 from both sides

• divide both sides by 2

• add 5 to both sides

• multiply both sides by 5

Answer explanation

Remember that a fraction is just a division sentence.  So  $\frac{n}{5}$  is the same as  $n\div5$  .  To get the variable by itself, we need to "undo" the division with the opposite operation.  So multiply both sides by 5.

Tags

CCSS.6.EE.B.7

Solve for y.

 $\frac{y}{3}=12$  

•  $y=36$  

•  $y=-36$  

•  $y=4$  

•  $y=-4$  

Answer explanation

 $\frac{y}{3}=12$  

Step 1: multiply both sides by 3 and simplify
 $y=36$  

Tags

CCSS.6.EE.B.7

Solve:

 $-9+2n=25$  

•  $n=21$  
  

•  $n=17$  

•  $n=-15$  

•  $n=-21$  

Answer explanation

 $-9+2n=25$  

Step 1: add 9 to both sides and simplify
 $2n=34$  

Step 2: divide both sides by 2 and simplify
 $n=17$  

Tags

CCSS.7.EE.B.4A

Solve for x.

 $5-2x=-15$  

•  $x=-6$  

•  $x=4$  

•  $x=10$  

•  $x=19$  

Answer explanation

 $5-2x=-15$  


Step 1: Subtract 5 from both sides and simplify
 $-2x=-20$  

Step 2: Divide both sides by -2 and simplify
 $x=10$  

Tags

CCSS.7.EE.B.4A

What is the first step to solve this equation?

 $8+\frac{a}{3}=11$  

• subtract 11 from both sides

• subtract 8 from both sides

• multiply both sides by 3

• divide both sides by 3

Answer explanation

Remember that the first step is to isolate the term with the variable on one side of the equal sign.

Tags

CCSS.7.EE.B.4A