Answer:
To solve the equation 5x - 4 = 3(x + 2) - 8, we can use several properties of equality. Here's the step-by-step solution:
1a) Show the work in each box that is required to get to the next given step:
A. 5x - 4 = 3(x + 2) - 8
B. 5x - 4 = 3x + 6 - 8
C. 5x - 4 = 3x - 2
D. 2x + 4 = -2
E. 2x = 2
F. x = 1
Step-by-step explanation:
Step A: Distributive Property is used to multiply 3 to both x and 2 inside the parentheses.
Step B: Addition Property of Equality is used to simplify the expression by combining like terms (6 - 8).
Step C: Subtraction Property of Equality is used to subtract 3x from both sides.
Step D: Addition Property of Equality is used to add 4 to both sides.
Step E: Division Property of Equality is used to divide both sides by 2.
Step F: Simplification is used to simplify the equation by reducing 2x/2 to x and 2/2 to 1.
1b) Property Used:
- Step A to Step B: Addition Property of Equality
- Step B to Step C: Simplification
- Step C to Step D: Subtraction Property of Equality
- Step D to Step E: Division Property of Equality
- Step E to Step F: Simplification
Final answer:
- The property used to get from Step E to Step F is Simplification by reducing 2/2 to 1.
1c) Verify algebraically that Pete's answer of x = 1 is a solution to the given equation in Step A. Show all work:
Substituting x = 1 into the equation:
5(1) - 4 = 3(1 + 2) - 8
1 = 3 - 8
1 = -5
Since 1 does not equal -5, Pete's answer of x = 1 is not a solution to the given equation in Step A.