Match the description of the one variable equation with the number of solutions it will have.
ax+c1=bx+c2
(3 points)
The number of x's on both sides of the equation is different a≠b
The number of x's is the same on both sides of the equation, and the constant is different a=b, c/1≠c/2
The number of x's is the same on both sides of the equation and the constant is also the same a=b, c/1=c/2
- The number of x's on both sides of the equation is different: 1 solution
- The number of x's is the same on both sides of the equation, and the constant is different: no solution
- The number of x's is the same on both sides of the equation and the constant is also the same: infinite solutions
Order the steps for solving the equation: 2x−5=3(4x+5)
(8 points)
2x−5=3(4x+5)
Step 1:
Distributive
Property to get
Step 2:
Property to get
Step 3:
Property to get
Step 4:
Property to get
Step 1: Distributive Property to get 2x-5=12x+15
Step 2: Combine like terms to get 2x-5=12x+15
Step 3: Subtraction Property to get 2x-12x=15+5
Step 4: Combine like terms to get -10x=20
1. The number of x's on both sides of the equation is different (a ≠ b) - This equation will have one solution.
2. The number of x's is the same on both sides of the equation, and the constant is different (a = b, c₁ ≠ c₂) - This equation will have no solution.
3. The number of x's is the same on both sides of the equation, and the constant is also the same (a = b, c₁ = c₂) - This equation will have infinitely many solutions.