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ivolga24 [154]
2 years ago
13

Explain how you know if an equation has no solutions, one solution or an infinite number of solutions

Mathematics
1 answer:
topjm [15]2 years ago
5 0

Answer:

If you cancel out all of the x terms via addition or subtraction, and you get something along the lines of 1 = 2, then you have no solution.

11x + 4 = 11x + 7 Subtract 11x from both sides

4 = 7 No value for x will satisfy this equation.

If you cancel out all the x terms via addition or subtraction and you get something along the lines of 1 = 1, then you have infinite solutions.

2(x + 1) = 2x + 2 Expand the left side using the distributive property

2x + 2 = 2x + 2 Subtract 2x from both sides

2 = 2 Every value for x will satisfy this equation

If you can’t cancel out all the x terms with addition or subtraction, you probably have 1 solution.

5x + 2 = 3x + 100 Subtract 3x from both sides

2x + 2 = 100 Subtract 2 from both sides

2x = 98 Divide by 2 on both sides

x = 49 The only x value that satisfies this equation is 49

There are other cases where functions of x aren’t injective, meaning there’s more than one x value that satisfies the equation. Here’s what I mean.

x^2 = 4

x = 2 or -2

x^3 = 1

x = 1, -1/2 + isqrt(3)/2, -1/2 - isqrt(3)/2

sin(x) = 0

x = 2n*pi, where n is some integer

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Enter your answer and show all the steps that you use to solve this problem in the space provided.
rodikova [14]

Answer:

\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}

Step-by-step explanation:

f(x) = 9x³ + 2x² - 5x + 4; g(x)=5x³ -7x + 4

Step 1. Calculate the difference between the functions

(a) Write the two functions, one above the other, in decreasing order of exponents.

ƒ(x) = 9x³ + 2x² - 5x + 4

g(x) = 5x³           - 7x + 4

(b) Create a subtraction problem using the two functions

        ƒ(x) =    9x³ + 2x² - 5x + 4

      -g(x) =  <u>-(5x³           - 7x + 4) </u>

ƒ(x) -g(x)=

(c). Subtract terms with the same exponent of x

        ƒ(x)   =    9x³ + 2x² - 5x + 4

      -g(x)  =   <u>-(5x³          -  7x + 4) </u>

ƒ(x) -g(x) =      4x³ + 2x² + 2x

Step 2. Factor the expression

y = 4x³ + 2x² + 2x

Factor 2x from each term

y = 2x(2x² + x + 1)

\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}

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2 years ago
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