Question

Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contraction or neither.
A) 20-4x=12-x+8-3x
B) 5x+4x-3+24+8x
C) 5x +6+2x+6+3x-15

Confusing please help

Answer 1

These are three equations and three answers.

Answers:

• A) infinite solutions, identity
• B) one solution, x = 27, neither contradiction nor identiy
• C) x = no solutions, contradiction

Explanation:

Equation A: 20 - 4x = 12 - x + 8 - 3x

The objective is clearing the unknown, which is to isolate it in one side of the equation.

These are the steps and properties that you need to use:

1.  Combine like terms on right side:

20 - 4x  = 20 - 4x

2. Use addition property of equality (add 4x on each side).

20 = 20 ↔ identity

Conclusion: you have gotten a condition that is always true, no matter the value of x, which means that the equation has infinite solutions and it is an identity.

Equation B: 5x + 4x - 3  =  24 + 8x (note that I placed the equal sign as it was missing)

1.  Combine like terms on each side:

9x - 3 = 24 + 8x

2. Subtraction property and addition propertiy of equality (subtract 8x and add + 3 on both sides)

x = 27 ↔ solution (neither contradiction nor identity)

Conclusion: the solution is x = 27.

Equation C: 5x + 6 = 2x + 6 + 3x - 15 (note that I placed the equal signs as it was missing)

1. Comitne like terms on the right side:

5x + 6 = 5x - 9

2. Subtraction property of equality (subtract 5x from each side)

6 = - 9 ↔ contradiction

Conclusion: the equation does not have a solution since the final equality is always false (a condradiction or absurd).

For your information, when the variable (x) dissapears and fhe final equality is always true (for example 0 = 0, or 20 = 20), the equation is an identity.

Answer 2

A) 20-4x=12-x+8-3x

Bring all x values at one side and all numerical values to the other side of the equal sign and solve. Also, do not forget to change the sign when you change the side.

-4x + x + 3x = -20 + 12 + 8

-4x + 4x = -20 + 20

0 =0 No solution

B) 5x+4x-3+24+8x

this expression can only be simplified to 17x + 21 and not solved because there is no equal sign here

C) 5x +6+2x+6+3x-15

this expression can only be simplified to 10x - 3 and not solved because there is no equal sign here

Also, neither of these is an identity or contraction.