The document shows the step-by-step work to solve the linear equation 3x^2 + 4 = 13. It begins by multiplying both sides by 2 to eliminate the fraction. It then distributes and combines like terms before subtracting and dividing to isolate x. The final solution is x = 6.

1. Linear Equations Example 1

2. Linear Equations Example 1
Find solutions to the equation:
3x
2 + 4 = 13

3. Linear Equations Example 1
Find solutions to the equation:
3x
2 + 4 = 13

4. Linear Equations Example 1
Find solutions to the equation:
3x
2 + 4 = 13

5. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13

6. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side

7. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 +4 − 4 = 13−4

8. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4

9. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9

10. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9

11. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9
Next, Multiply by 2 on each side

12. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9
Next, Multiply by 2 on each side
2 · 3x
2 = 2·9

13. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9
Next, Multiply by 2 on each side
3x = ¡2 · 3x
¡2
= 2·9

14. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9
Next, Multiply by 2 on each side
3x = ¡2 · 3x
¡2
= 2·9 = 18

15. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9
Next, Multiply by 2 on each side
3x = ¡2 · 3x
¡2
= 2·9 = 18
3x = 18

16. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9
Next, Multiply by 2 on each side
3x = ¡2 · 3x
¡2
= 2·9 = 18
3x = 18
Finally, we will Divide by 3 on each side to get

17. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9
Next, Multiply by 2 on each side
3x = ¡2 · 3x
¡2
= 2·9 = 18
3x = 18
Finally, we will Divide by 3 on each side to get
3x
3 = 18
3

18. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9
Next, Multiply by 2 on each side
3x = ¡2 · 3x
¡2
= 2·9 = 18
3x = 18
Finally, we will Divide by 3 on each side to get
x = ¡3x
¡3
= 18
3

19. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9
Next, Multiply by 2 on each side
3x = ¡2 · 3x
¡2
= 2·9 = 18
3x = 18
Finally, we will Divide by 3 on each side to get
x = ¡3x
¡3
= 18
3 = 6

20. Linear Equations Example 1
Find solutions to the equation:
3x
2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x
2 = 3x
2 $$$$+4 − 4 = 13−4 = 9
3x
2 = 9
Next, Multiply by 2 on each side
3x = ¡2 · 3x
¡2
= 2·9 = 18
3x = 18
Finally, we will Divide by 3 on each side to get
x = ¡3x
¡3
= 18
3 = 6
The solution to the equation is x = 6

21. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13

22. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.

23. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13

24. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26

25. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.

26. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
2 · 3x
2 + 2·4 = 2 · 3x
2 +4 = 2·13 = 26

27. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26

28. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26

29. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides

30. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides
3x + 8−8 = 26−8

31. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8

32. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 18

33. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 18
3x = 18

34. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 18
3x = 18
Finally, we will Divide by 3 on each side to get

35. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 18
3x = 18
Finally, we will Divide by 3 on each side to get
3x
3 = 18
3

36. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 18
3x = 18
Finally, we will Divide by 3 on each side to get
x = ¡3x
¡3
= 18
3

37. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 18
3x = 18
Finally, we will Divide by 3 on each side to get
x = ¡3x
¡3
= 18
3 = 6

38. Linear Equations Example 1 Return to original problem
Find solutions to the equation:
3x
2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
2 · 3x
2 +4 = 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = ¡2 · 3x
¡2
+ 2·4
8
= 2 · 3x
2 +4 = 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 18
3x = 18
Finally, we will Divide by 3 on each side to get
x = ¡3x
¡3
= 18
3 = 6
The solution to the equation is x = 6