Question

Find the number of real solutions to the functions below

Answer 1

7) x + 3 = (x - 5)2:  x = 13

Let's start with this part of the equation:

(x - 5) x 2

Switch:

= 2(x - 5)

Apply the distributive law: a(b - c) = ab - ac

a = 2, b = x, c = 5

= 2x - 2 x 5

Multiply the numbers: 2 x 5 = 10

= 2x - 10

Plug in the expression:

x + 3 = 2x - 10

Subtract 3 from both sides

x + 3 - 3 = 2x - 10 - 3

Simplify

x = 2x - 13

Subtract 2x from both sides

x - 2x = 2x - 13 - 2x

Simplify

-x = -13

Divide both sides by -1

-x / -1  =  -13 / -1

Simplify

x = 13

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8) x4 = x - 10:  x = -10/3  or  x = 3.33(repeating)

Let's rewrite this equation:

x * 4 = x - 10

Subtract x from both sides

x * 4 - x = x - 10 - x

Simplify

3x = -10

Divide both sides by 3

3x / 3 = -10 / 3

Simplify

x = -10/3 - as a fraction

x = 3.33(repeating) - as a decimal

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9)  x3 = 5 – x :  x = 5/4  or  x = 1.25

Let's rewrite this equation:

x * 3 = 5 - x

Add x to both sides

x * 3 + x = 5 - x + x

Simplify

4x = 5

Divide both sides by 4

4x / 4 = 5 / 4

Simplify

x = 5/4 - as a fraction

x = 1.25 - as a decimal