(03.05 MC) Solve the rational equation x divided by 2 equals x squared divided by quantity x minus 2 end quantity, and check for extraneous solutions. No solution x = 0 and x = −2 x = −2; x = 0 is an extraneous solution x = 0; x = −2 is an extraneous solution

x = 0 and x = -2 are solutions of the given rational equation.

Step-by-step explanation:

We must solve the following rational equation:

Now we present the procedure:

1) Given

2) Compatibility with multiplication/Existence of the multiplicative inverse/Definition of division/Modulative property.

3) Distributive property/

4) Compatibility with addition/Existence of the additive inverse/Modulative property/Reflexive property

5) Distributive property/

6) Result

Now we check the rational equation with each root:

x = 0

x = 0 is a solution of the rational equation.

x = -2

x = -2 is a solution of the rational equation.

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step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: