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klio [65]
2 years ago
12

Variable termes X-12-3X+22

Mathematics
1 answer:
adell [148]2 years ago
7 0

Answer: x + 12 = 3x + -22

12 + x = 3x + -22

Reorder the terms:

12 + x = -22 + 3x

Solving

12 + x = -22 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

12 + x + -3x = -22 + 3x + -3x

Combine like terms: x + -3x = -2x

12 + -2x = -22 + 3x + -3x

Combine like terms: 3x + -3x = 0

12 + -2x = -22 + 0

12 + -2x = -22

Add '-12' to each side of the equation.

12 + -12 + -2x = -22 + -12

Combine like terms: 12 + -12 = 0

0 + -2x = -22 + -12

-2x = -22 + -12

Combine like terms: -22 + -12 = -34

-2x = -34

Divide each side by '-2'.

x = 17

Simplifying

x = 17

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Calculate the area of rectangle:

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Answer:

The conclusion "T" logically follows from the premises given and the argument is valid

Step-by-step explanation:

Let us use notations to represent the steps

P: I take a bus

Q: I take the subway

R: I will be late for my appointment

S: I take a taxi

T: I will be broke

The given statement in symbolic form can be written as,

(P V Q) → R

S → (¬R ∧ T)

(¬Q ∧ ¬P) → S

¬R

___________________

∴ T

PROOF:

1. (¬Q ∧ ¬P) → S                Premise

2. S → (¬R ∧ T)                  Premise

3. (¬Q ∧ ¬P) → (¬R ∧ T)    (1), (2), Chain Rule

4. ¬(P ∨ Q) → (¬R ∧ T)      (3), DeMorgan's law

5. (P ∨ Q) → R                   Premise

6. ¬R                                 Premise

7. ¬(P ∨ Q)                        (5), (6), Modus Tollen's rule

8. ¬R ∧ T                          (4), (7), Modus Ponen's rule

9. T                                   (8), Rule of Conjunction

Therefore the conclusion "T" logically follows from the given premises and the argument is valid.

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3 years ago
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