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