Answer:
7. r = -5
8. x = -1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Explanation:
Step 1: Define
r + 2 - 8r = -3 - 8r
Step 2: Solve for r
- Combine like terms: -7r + 2 = -3 - 8r
- Add 8r to both sides: r + 2 = -3
- Subtract 2 on both sides: r = -5
Step 3: Check
Plug in r into the original equation to verify it's a solution.
- Substitute in r: -5 + 2 - 8(-5) = -3 - 8(-5)
- Multiply: -5 + 2 + 40 = -3 + 40
- Add: -3 + 40 = -3 + 40
- Add: 37 = 37
Here we see that 37 does indeed equal 37.
∴ r = -5 is a solution of the equation.
Step 4: Define equation
-4x = x + 5
Step 5: Solve for x
- Subtract x on both sides: -5x = 5
- Divide -5 on both sides: x = -1
Step 6: Check
Plug in x into the original equation to verify it's a solution.
- Substitute in x: -4(-1) = -1 + 5
- Multiply: 4 = -1 + 5
- Add: 4 = 4
Here we see that 4 does indeed equal 4.
∴ x = -1 is a solution of the equation.