Equations with Variables on both sides
3x - 6 = 5x
x = 3
Mr. Carter is building a rectangular garden. The length of the garden is 5 feet longer than its width. If the perimeter of the garden is 46 feet, what is the width of the garden?
Width = 9 feet
3(2x − 4) = 5x + 6
x = 18
How many solutions? If one solution, please solve.
2x + 3 = x + 7
One solution
x=4
Fill in the blanks:
1. An equation with no solution has _____ coefficient and _____ constant.
2. An equation with infinite solutions has _____ coefficient and _____ constant.
3. An equation with one solution has _____ coefficient and _____ constant.
1. same, different
2. same, same
3. different, same/different
2x + 7 = 4x - 1
x = 4
A group of 4 people each paid an entrance fee of x dollars and 4 dollars for snacks to a soccer game. Another group of 3 people went to a football game where they paid twice as much for entrance as the soccer game and paid 4 dollars each for snacks. Both groups of people spent the same total amount. What was the entrance fee per person for the soccer game?
Entrance fee for the soccer game is $4.
4(3x + 2) − 5x = 2(x + 7) + 3
x = 9/5
How many solutions? If one solution, please solve.
5(x - 2) = 5x - 10
Infinite Solutions
What numbers would fill in the blank in order to have infinite solutions?
3x + 9 = ___x + ____
Coefficient is 3 and constant is 9.
0.5x + 3 = 0.3x + 11
x = 40
A rectangular playground has a length that is 3 meters less than three times its width. If the perimeter of the playground is 72 meters, find the length of the playground.
2(5x − 3) + 4x = 3(2x + 1) + 7
x = 2
How many solutions? If one solution, please solve.
4(x + 1) = 4x + 5
No Solution
What numbers would fill in the blank in order to have no solutions?
3x + 9 = ___x + ____
Coefficient is 3 and constant is any number not equal to 9.
1/2 x + 4 = 1/4 x - 4
x = -32
Six coworkers each paid x dollars for a workshop and 4 dollars for coffee. Four coworkers attended a different workshop, paying twice as much for admission and 3 dollars for coffee. Both groups paid the same total amount. Find the total cost of 1 person to attend the first workshop.
The cost for one person to attend the first workshop is $10. $6 admission fee and $4 coffee.
5(4x − 2) + 3x = 2(7x + 1) − 8
x = 4/9
How many solutions? If one solution, please solve.
3(2x - 4) = 2(3x - 6)
Infinite solutions
What numbers would fill in the blank in order to have infinite solutions?
4(x + 3) = ___x + ____
Coefficient is 4 and constant is 12.
1/3 x + 5 = 2/5 x + 10
x = -75
The length of a rectangular pool is 8 feet more than its width. If the perimeter is 84 feet, what is the area of the pool?
Area of the pool is 425 square feet.
Width is 17 feet and the length is 25 feet.
6(2x + 1) − 4(x − 3) = 3(3x + 2) + 5
x = 7
2(3x + 1) - 4 = 6x + 5 + 0x
No Solution
What numbers would fill in the blank in order to have no solutions?
8(2x + 2) + 9x - 4 = ___x + ____
Coefficient is 25 and constant is any number not equal to 12.