solve the equation 2x + 4 = –3x + 14. Examine the work of and Identify any errors made explain, using complete sentences, what corrections they should make.

Question

Algebra 1 review word problem 

Answer 1

2x + 4 = -3x +14

2x+3x =14 - 4    Reorganizing

5x = 10             Grouping similar terms

x = 10/5            Isolating the X

x= 2                  Simplifying the fraction

What it means

The value of x=2 is a vertical line in the X-plane that go through   x=2. You can assign different values to the variable y but the value of X remains the same.

Thanks

Answer 2

So, let me add another perspective.

You have two linear equations y = 2x+4 and y = -3x+14 and they are set equal to one another such that 2x +4 = -3x +14, but not in the sense that both equations produce the same line. However, you are looking for a unique value of x that when placed in each equation produces the same value of y.

When you solve the equation 2x +4 = -3x + 14, you find that x =2.

When x =2, you have y = 2(2) +4 = 8 and y = -3(2) +14 = 8.

If you graph 2x +3 and -3x +14 their lines will intersect at the coordinates (2,8)

Also, if you looked at the graph first you could the use the coordinates of the point of intersection and work backwards to solve the problem.

Answer 3

2X + 4 = -3X + 14

 

Bring -3X over to the left side. 

 

2X + 4 + 3X = 14

 

5X + 4 = 14

 

subtract 4 from both sides

 

5X = 14 - 4

 

5X = 10

 

divide both sides by 5

 

X = 2.

 

 

Answer 4

2x + 4 = -3x + 14      Add 3x to both sides

5x + 4 = 14               Subtract 4 from both sides

5x = 10                      Divide both side by 5

x = 2