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5. Find all the values for the variable that make each equation true.

a. b(b-4.5) = 0
b. (7x+14)(7x+14) = 0
c. (2x + 4)(x-4)=0
d. (-2+u)(3-u) = 0

1 Answer

5 votes

Answer:

a: b = 0, 4.5

b: x = -2

c: x = -2, 4

d: u = 2, 3

Explanation:

We can use the zero product property for all of these equations. These equations are given to us already factored, so now we just need to solve them.

a:

Given:

b(b - 4.5) = 0

Zero product property:

b = 0 & b - 4.5 = 0

Add 4.5 to both sides of the right equation:

b = 0 & b = 4.5

b = 0, 4.5

b:

Given:

(7x + 14)(7x + 14) = 0

Zero product property:

➜ Here, it's the same equation.

7x + 14 = 0 & 7x + 14 = 0

Subtract 14 from both sides of the equation:

7x = -14

Divide both sides of the equation by 7:

x = -2

c:

Given:

(2x + 4)(x - 4)=0

Zero product property:

2x + 4 = 0 & x - 4 = 0

Isolate the variable x in each instance by subtracting from both sides in the left and adding 4 to both sides in the right:

2x = -4 & x = 4

Divide both sides of the left equation by 2:

x = -2 & x = 4

x = -2, 4

d:

Given:

(-2 + u)(3 - u) = 0

Zero product property:

-2 + u = 0 & 3 - u = 0

Isolate the variable u in each instance by adding 2 to both sides in the left and u to both sides in the right:

u = 2 & u = 3

u = 2, 3

User Alex Wohlbruck
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