Solving For a Variable
2x+4+3+2x=12+7
x=3
Simplify the following equation and then determine how many solutions there are.
2x+2+6=3x+1-x+5
2x+8=2x+6
No Solution
At the store, if you buy 7 apples it will cost $3.43. How much is each apple?
Each apple is $0.49
From the following equation, identify the slope.
y= -1/3x
m= -1/3
What do the variables m and b represent in the equation y=mx+b
m=slope
b=y-int
8.63x+9.42x=126.35
x=7
Simplify the following equation and then determine how many solutions there are.
2(3x+4)=4+3(x+4)
6x+8=3x+16
One Solution
At the gas station, Ella pumped 12 gallons of gas and the total was $21. How much is each gallon of gas?
Each gallon is $1.75
How do you tell where the y-int is on a graph?
Describe how to plot the equation y=mx+b
use the slope(m) to plot the final 2 points
3(x+5)-3=4+2(x+1)
x=-6
Simplify the following equation and then determine how many solutions there are.
0.25(2x+8)=1+0.25(4x+4)-0.5x
0.5x+2=0.5x+2
Infinitely Many Solutions
Cameron ran 9 miles in 67.5 minutes. How long does it take him to run 1mile?
He can run 1 mile in 7.5 mins
What variable from the following equation represents the y-int.
y=mx+b
b is the y-int
Graph the following equation:
y=x+3
plot the 1st point at 3
use the slope of 1 to plot the final 2 points
4(2x+4)-3=5+2(x+3)
x= -1/2
Simplify the following equation and then determine how many solutions there are.
9x+3-2x+4=3x+2+x+3+3x+2
7x+7=7x+7
Infinitely Many Solutions
Becky and Lucy are going to get gas. Becky paid $29.55 for 15 gallons of gas. Lucy paid $42.21 for 21 gallons of gas. Who paid less per gallon of gas and how much did they pay?
Becky paid $1.97/gal and Lucy paid $2.01/gal
Becky paid less per gallon
Graph the following equation:
y=3/2x
Plot the 1st point at (0,0)
use the slope 3/2 to plot the next 2 points
Graph the following equation:
y=3/4x-4
plot the first point at -4
use the slope 3/4 to plot the final 2 points
3/2(4x+3)= 1/4(8x+4)
x= -1/4
Simplify the following equation and then determine how many solutions there are.
2/3(9x+3)=3/5(10x+5)
6x+2=6x+3
No Solution
Luke can run 12 miles in 87 minutes. Roger can run 9 miles in 67.5 minutes. How long does it take each of them to run a mile? Who can run a mile faster?
Luke can run a mile in 7.25 minutes and Roger can run a mile in 7.5 minutes.
Luke runs a mile faster
Graph the following equation:
y= -5/4x
Plot the first point at (0,0)
use the slope -5/4 to plot the final 2 points
Graph the following equation:
x=-4
plot a point at -4 on the x-axis. Since it is not our normal equation, this equation will create a vertical line.