How stuff works
List the steps used when solving Multi-Step Linear Equations with variables on each side.
1. Distributive property (if needed)
2 Combine like terms (if needed)
3. +,- to get variables on one side
4. +,- to eliminate constant
5. divide to eliminate coefficient on the variable term.
Solve 6n − 1= 4n − 5.
Determine whether the equation has one solution, no solution, or infinitely many solutions.
One solution
(n=-2)
Why can two floor plans with perimeters 4x+12 and 4x+10 never have equal perimeters?
No value of x will make 4x+12=4x+10. (Because when you subtract the 4x from both sides you get 12=10 which is not true.)
Why will two floor plans with perimeters 2(2x+6) and 4x+12 always have equal perimeters?
Because when you distribute 2(2x+6) you get 4x+12 which is the same as 4x+12. So any value substituted for x will still give you the same thing.
Solve 8(x − 9) = 6(2x − 12) − 4x. Determine whether the equation has one solution, no solution, or infinitely many solutions.
Infinitely many solutions
How many solutions are there when both sides of the equation simplify to matching variable terms and matching constant terms.
Infinite many solutions
Solve. 8 + 3x = 5x + 2
Determine whether the equation has one solution, no solution, or infinitely many solutions.
One solution
(x=3)
What number(s) would complete the equation so that it has no solutions?
3k+7=3k+?
anything but 7
What numbers would complete the equation so that it has infinitely many solutions?
6x -3 =?x-3
6
Solve 24x + 36- 15x=6-6x.
Determine whether the equation has one solution, no solution, or infinitely many solutions.
one solution
How many solutions are there when both sides of the equation simplify to matching variable terms but NOT matching constant terms.
No solutions
What is a constant or variable term that makes the equation have one solution?
3x+2=?
any amount of "x" except "3x"
What number(s) would complete the equation so that it has no solutions?
5x-8=?x-?
5 and NOT 8
(5x-anything but 8)
What numbers would complete the equation so that it has infinitely many solutions?
7x+15+3=?x+?
7 and 18
(7x+18)
Solve - 2(x + 3) = 4(x + 1) -6x - 5
Determine whether the equation has one solution, no solution, or infinitely many solutions.
No solution
How many solutions are there when both sides of the equation simplify to NOT matching variable terms and NOT matching constant terms.
One solution
What is a constant or variable term that makes the equation have one solution?
3x+2=3x+?
any amount of "x"
(combine like terms and then there will be a different amount of "x"s on each side.)
What number(s) would complete the equation so that it has no solutions?
-2x-6=?x-?
-2 and NOT 6
(-2x-anything but 6)
What numbers would complete the equation so that it has infinitely many solutions?
?p+5=5-4p
-4
Solve 2(3c − 6) − 2c = 4(c + 4). Determine whether the equation has one solution, no solution, or infinitely many solutions.
No solution
How many solutions are there when both sides of the equation simplify to NOT matching variable terms but matching constant terms.
One Solution
(the solution will be x=0)
Solve 15 − (7x + 20) = 0.5(6x − 14).
Determine whether the equation has one solution, no solution, or infinitely many solutions.
One solution
(x=0.2)
Write an equation that has no solution
Any equation with the same number of variables on both sides of the equal sign but a different number of constants.
What numbers would complete the equation so that it has infinitely many solutions?
6x − x + 4 + 2x = (?) x + (?)
7x + 4
Solve. −10y + 18 = −3(5y − 7) + 5y
Determine whether the equation has one solution, no solution, or infinitely many solutions.