Solve Equations with Variables on Each Side
3x + 6 = 4x + 3
x = 3
Company A charges a $10 shipping fee and $2 per pound. Company B charges a $12 shipping fee and $1.50 per pound. How many pounds is the cost the same for both companies?
4
Solve for x.
4(2x - 2) + 6x = 5(3x - 2) - 7
x = 9
DOUBLE JEOPARDY
If both sides of an equation have the same coefficients but different constants, how many solutions will the equation have? How do you know?
When the coefficients are the same but the constants are different that means there will be No Solution.
Company A pays $3500 plus $275 per car sold. Company B pays $3000 plus $350 per car sold. Create an equation that compares company A with company B?
3500 + 275x = 3000 + 350x
DOUBLE JEOPARDY
Furnace A is at a temperature of 1400 degrees and cools at a rate of 25 degrees per minute. Furnace B is at a temperature of 1200 degrees and is heated at a rate of 15 degrees per minute. After how many minutes will the furnaces be at the same temperature?
5 minutes
DOUBLE JEOPARDY
Solve for x.
0.1(x+6) -0.7x=0.4(2x-2)+8.4
x = -5
How many solutions?
4(2x + 1 ) = 5(x + 2) + 3
One solution
Double Jeopardy
-0.25a + 3.8 = 0.5a - 5.2
A. Solve.
B. Check Your Solution and show your work.
a = 12
0.8 = 0.8
7 students went bowling and each rented shoes for $x and $15 on snacks. 6 adults paid twice as much for shoes and $12.50 on snacks. If both groups spent the same amount how much did each adult pay for shoes?
$12
Solve for x.
-2(4x + 6) + 4 = 2(5x - 9) - 8x
x = 1
Complete the equation that will result in infinitely many solutions.
8x + 2(3x + 1) = _____x + _____
14x + 2
4/5d - 5 = 3/5d - 2
d = 15
The width of a rug was 3 and 1/4 inches longer than twice its length. The perimeter of the rug is 54 and 1/2 inches. Which equation represents this situation?
54 1/2 = L + L + (3 1/4 + 2L) + (3 1/4 + 2L)
54 1/2 = 2L + 2(3 1/4 + 2L)
54 1/2 = 6L + 6 1/2
Solve for x.
0.3(4q - 6) + 2.7 = -0.2(q+4)+4.5
q = 2
Complete the equation that will result in "No Solution".
5x - 2(3x + 6) = _____x - _____
A.-5 and 6 B.-1 and 12 C.5 and 12 D.-1 and 6
-1x - 6
-2.7x + 3.5=1.3x + 11.5
x = -2
The length of a frame is 4 inches shorter than its width. The perimeter of the frame is 44 inches. What is the length and width of the picture frame?
Length = 9 inches
Width = 13 inches
9 students go to an amusement park and pay $2x for admission and go on 1 ride that costs $1, 14 students go to a water park and pay $x for admission and go on 1 ride that costs $3.50. The total is the same for each group. What is the admission price for the amusement park for each student?
x = $20
One solution, Infinite solutions, or No Solutions
A. 3(4x-4)=4(3x-3)
B. 2(5x+3)=6(x+8)+2
C. 4(x-5)=2(9+2x)
A. Infinite Solutions
B. One Solution
C. No Solution