Bellwork Bellwork 1.What is a solution to an equation or inequality? 2.Determine whether 2/3 is a solution to this equation: 3x - 10 = - 8. 3. Determine if -1/2 is a solution to 4x – 3 < -12 ?
Dec 17, 2015
BellworkBellwork1.What is a solution to an equation or
inequality?
2.Determine whether 2/3 is a solution to this equation: 3x - 10 = -8.
3. Determine if -1/2 is a solution to 4x – 3 < -12 ?
VocabularyVocabulary Equation: a mathematical
sentence that contains an equal sign.
Inequality: a mathematical sentence that contains an inequality symbol.
Solution: a number that makes the sentence true.
To solve an To solve an Equation/Inequality:Equation/Inequality:
Isolate the variable!
Don't forget to flip the inequality symbol if you multiply or divide by a negative
Always write the variable on the left when finished with the problem.
3 Types of Solutions to 3 Types of Solutions to EquationsEquations
1. The equation has ONE REAL solution
(which will be x = #)
2. The equation has ANY REAL NUMBER as a solution
(which will be 0 = 0)
3. The equation has NO REAL solution
(which will be 0 = #)
1. 3/7 x + 9 = 15
- 9 - 9
3/7x = 6
7/3(3/7x) = 6 (7/3)
x = 14
2. 5n + 11 = 7n - 9
- 11 - 11
5n = 7n -20
-7n -7n
-2n = -20 -2 -2 n = 10
Solve each, then check your solutionSolve each, then check your solution
4(3x - 5) = -2(-x + 8) - 6x
12x - 20 = 2x - 16 - 6x
12x - 20 = - 4x - 16 + 20 + 20 12x = -4x + 4 +4x +4x 16x = 4 16 16 x = 1/4
4. 1/3x + 1/4 = X - 1/6
12(1/3x + 1/4 = X - 1/6)
4X + 3 = 12X - 2
- 3 -3
4X = 12X - 5
-12X -12X
-8X = -5
-8 -8
X = 5/8
Solve each, then check your solutionSolve each, then check your solution 3.
5. -4(6x - 5) = 23 - 3(8x + 1)
-24x + 20 = 23 – 24x – 3
-24x + 20 = 20 – 24x
- 20 -20
-24x = -24x
+ 24x +24x
0 = 0
All real numbers
6. -2x - (x + 3) = 3x – 3
-2x – x – 3 = 3x – 3
-3x – 3 = 3x – 3
+ 3 + 3
-3x = 3x + 0
-3x -3x
-6x = 0
-6 -6
X = 0
Solve each, then check your solutionSolve each, then check your solution
Solve each, then check your solutionSolve each, then check your solution
7. -2/3(6/5x - 7/10) = 17/20
-12/15x + 7/15 = 17/20
60(-12/15x + 7/15 = 17/20)
-48x + 28 = 51
-28 -28
-48x = 23
-48 -48
X = - 23/48
8. 2(x - 7) + 3 = 2x – 14
2X – 14 + 3 = 2x –14
2X – 11 = 2x – 14
+ 11 + 11
2X = 2x – 3
-2x -2x
0 = -3
No Solution!
Without solving...Without solving...
Tell whether the equation below has no solution, one solution, or any real solution, then explain.
a) 5x + 2 = 5x + 2 _____________
b) 5x + 2 = 2 – 5x _____________
c) 3x – 2 = 3x _____________
d) 2(x – 7) + 3 = 2x + 14 _____________
e) 3(2x – 1) = 6x – 3 _____________
One, X = #
No Sol, 0 = #
No Sol, 0 = #
ARN, 0=0
ARN, 0 = 0
Types of Solutions to Types of Solutions to InequalitiesInequalities
Set Notation Interval Notation
Graph
X < # (-∞ , # )
X < # (-∞ , # ]
X > # (#,∞)
X > # (#,∞ ]
Solve and graph each on a number line. Put Solve and graph each on a number line. Put
the answers in interval notation.the answers in interval notation. 1. 5y – 8 < 12 5Y < 20 Y < 4
(-∞, 4)
2. 2x + 1 < 6x – 1 -4x < -2 X > ½
[ ½,∞)
Solve and graph each inequality. Write the solution in Solve and graph each inequality. Write the solution in interval notation. interval notation.
3. 3 < 2/3 x + ½ 18 < 4x + 3 15 < 4x 15/4 < x X > 15/4 ( 15/4, ∞)
4. 7x + 9 > 10x – 12 -3x > -21 X < 7 (-∞, 7]
Solve and graph each inequality. Write the solution in Solve and graph each inequality. Write the solution in interval notation. interval notation.
5. 1/3(5/8x + 2) > 2/3 x + 2 5/24x + 2/3 > 2/3x + 2 24[5/24x + 2/3 > 2/3x + 2] 5x + 16 > 16x + 48 -11X > 32 x < -32/11 ( -∞, -32/11]
4. 4(1/2x + 7/3) > 1/3(x + 12) 2x + 28/3 > 1/3x + 4 3[2x + 28/3 > 1/3x + 4] 6x + 28 > x + 12 5X > -16 X > -16/5 (-16/5, ∞)
Mack works at an appliance store. He earns a base salary of $16,000 plus 12% of the total value of the appliances he sells for the year (commission). Last year he earned $18,800. What was the total value of the appliances he sold?
Coach Barr has decided to put a walking track of uniform width around the outside of the football field and then fence in the entire area. The football field is 160 ft by 300 ft and he has 968 ft of fencing to put around the entire area (football field AND walking track). What is the maximum width of the walking track?
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