Simplifying Expressions
Simplify:
3x+5x
8x
Solve:
x+5=12
x = 7
Solve:
2x+3=11
How many solutions?
One solution
Find the unit rate:
x = 1, y = 6
6
Simplify:
−2.5x+4x
1.5x
Solve:
3x=18
x = 6
Solve:
4x+2=4x+9
How many solutions?
No solution
Is this proportional?
x: 2, 4, 6
y: 6, 12, 18
Yes
Simplify:
3(x+4)
3x + 12
Solve:
2x+3=11
x = 4
Solve:
3(x+2)=3x+6
How many solutions?
Infinitely many solutions
Find the unit rate:
x: 3, 6, 9
y: 12, 24, 36
4
Simplify:
−1/2(6x−8)
-3x + 4
Solve:
2(x+3)=14
x = 4
What does it mean if you get a false statement like 5=9?
No solution
Write the equation of a proportional relationship with unit rate 4.
y=4x
A student says:
4(x+2)=4x+2
What is the mistake?
They didn’t distribute to both terms (should be 4x + 8)
Solve:
3x+5=x+17
x = 6
How can you tell an equation will have infinitely many solutions without solving completely?
Both sides simplify to the same expression
A line does not pass through (0,0). Is it proportional? Why or why not?
No, proportional relationships must pass through the origin