SAT
Solve for x. Find the equation with exactly one solution.
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Solve for x.
Get all the variables on one side and all the numbers on the other side.
If x equals a number, there is exactly one solution. Any number counts.
x equals a number
| 4x + 3 | = | x + 12 |
| 3x + 3 | = | 12 |
| 3x | = | 9 |
| x | = | 3 |
x = 3. There is exactly one solution.
x = 0
| 6x + 2 | = | 2x + 2 |
| 4x + 2 | = | 2 |
| 4x | = | 0 |
| x | = | 0 |
x = 0 is a number.
Infinite solutions
| 4x + 5 | = | 4x + 5 |
| 5 | = | 5 |
5 = 5. Math Truth! Infinite solutions.
No solution
| 2x + 3 | = | 2x + 7 |
| 3 | = | 7 |
3 = 7. Math Lie! No Solutions.
Work these three in a session.
Which equation has exactly one solution?
| A. | 4x + 9 | = | 4x + 2 |
| 9 | = | 2 | |
| Math Lie! No Solution | |||
| B. | 6x + 5 | = | 6x + 5 |
| 5 | = | 5 | |
| Math Truth! Infinite Solution! | |||
| C. | 5x + 1 | = | 2x + 13 |
| 3x + 1 | = | 13 | |
| 3x | = | 12 | |
| x | = | 4 | |
| One Solution! | |||
| D. | 3x − 4 | = | 3x + 7 |
| −4 | = | 7 | |
| Math Lie! No Solution | |||
Answer: C. 5x + 1 = 2x + 13
Which equation has exactly one solution?
| A. | 8x + 5 | = | 3x + 5 |
| 5x + 5 | = | 5 | |
| 5x | = | 0 | |
| x | = | 0 | |
| One Solution! | |||
| x = 0 is exactly one solution. Zero is a number. | |||
| B. | 8x + 3 | = | 8x − 6 |
| 3 | = | −6 | |
| Math Lie! No Solution | |||
| C. | x + 9 | = | x + 9 |
| 9 | = | 9 | |
| Math Truth! Infinite Solution! | |||
| D. | 5x + 2 | = | 5x + 14 |
| 2 | = | 14 | |
| Math Lie! No Solution | |||
Answer: A. 8x + 5 = 3x + 5
Which equation has exactly one solution?
| A. | 7x − 3 | = | 7x − 3 |
| −3 | = | −3 | |
| Math Truth! Infinite Solution! | |||
| B. | 4x + 6 | = | 4x + 1 |
| 6 | = | 1 | |
| Math Lie! No Solution | |||
| C. | 9x + 8 | = | 9x − 2 |
| 8 | = | −2 | |
| Math Lie! No Solution | |||
| D. | 6x − 5 | = | 2x + 7 |
| 4x − 5 | = | 7 | |
| 4x | = | 12 | |
| x | = | 3 | |
| One Solution! | |||
Answer: D. 6x − 5 = 2x + 7
Try these five on your own.
Which equation has exactly one solution?
| A. | 2x − 7 | = | 2x + 5 |
| −7 | = | 5 | |
| Math Lie! No Solution | |||
| B. | 8x − 4 | = | 2x + 8 |
| 6x − 4 | = | 8 | |
| 6x | = | 12 | |
| x | = | 2 | |
| One Solution! | |||
| C. | 6x + 1 | = | 6x + 1 |
| 1 | = | 1 | |
| Math Truth! Infinite Solution! | |||
| D. | 4x + 10 | = | 4x − 8 |
| 10 | = | −8 | |
| Math Lie! No Solution | |||
Answer: B. 8x − 4 = 2x + 8
Which equation has exactly one solution?
| A. | 5x + 6 | = | 5x + 6 |
| 6 | = | 6 | |
| Math Truth! Infinite Solution! | |||
| B. | 3x − 9 | = | 3x + 2 |
| −9 | = | 2 | |
| Math Lie! No Solution | |||
| C. | 7x + 4 | = | 7x − 1 |
| 4 | = | −1 | |
| Math Lie! No Solution | |||
| D. | 5x − 6 | = | 2x − 6 |
| 3x − 6 | = | −6 | |
| 3x | = | 0 | |
| x | = | 0 | |
| One Solution! | |||
| x = 0 is exactly one solution. Zero is a number. | |||
Answer: D. 5x − 6 = 2x − 6
Which equation has exactly one solution?
| A. | −5x + 4 | = | x + 16 |
| −6x + 4 | = | 16 | |
| −6x | = | 12 | |
| x | = | −2 | |
| One Solution! | |||
| B. | −4x + 7 | = | −4x + 2 |
| 7 | = | 2 | |
| Math Lie! No Solution | |||
| C. | −6x − 1 | = | −6x − 1 |
| −1 | = | −1 | |
| Math Truth! Infinite Solution! | |||
| D. | 5x + 8 | = | 5x − 3 |
| 8 | = | −3 | |
| Math Lie! No Solution | |||
Answer: A. −5x + 4 = x + 16
Which equation has exactly one solution?
| A. | 9x + 4 | = | 9x + 4 |
| 4 | = | 4 | |
| Math Truth! Infinite Solution! | |||
| B. | 2x − 5 | = | 2x + 11 |
| −5 | = | 11 | |
| Math Lie! No Solution | |||
| C. | 7x − 6 | = | 4x + 9 |
| 3x − 6 | = | 9 | |
| 3x | = | 15 | |
| x | = | 5 | |
| One Solution! | |||
| D. | −3x + 8 | = | −3x − 4 |
| 8 | = | −4 | |
| Math Lie! No Solution | |||
Answer: C. 7x − 6 = 4x + 9
Which equation has exactly one solution?
| A. | 6x − 8 | = | 6x + 4 |
| −8 | = | 4 | |
| Math Lie! No Solution | |||
| B. | 6x − 8 | = | 2x + 12 |
| 4x − 8 | = | 12 | |
| 4x | = | 20 | |
| x | = | 5 | |
| One Solution! | |||
| C. | 6x − 8 | = | 6x − 8 |
| −8 | = | −8 | |
| Math Truth! Infinite Solution! | |||
| D. | 2x + 12 | = | 2x − 8 |
| 12 | = | −8 | |
| Math Lie! No Solution | |||
Answer: B. 6x − 8 = 2x + 12
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