Suppose a room measures 16 feet long by 12 feet wide by 7 feet high and has two windows and a door. How many gallons of paint are needed to paint the room? To solve this problem, first find the square footage of the room. The sum of the wall lengths is the perimeter of the room.
Now solve the equation to find x.
x = 2(16 + 12) ⋅ 7 – (15 + 15 + 15) Original
equation
x = 2(28) ⋅ 7 – 45 Simplify inside the
parentheses.
x = 56 ⋅ 7 – 45 Multiply 2 and
28.
x = 392 – 45 Multiply 56
and 7.
x = 347 Subtract
45 from 392.
The room has an area of 347 square
feet. Therefore, only one gallon of paint is needed to paint the room.
In solving the equation above, the
first step was to remove the parentheses. This is often the first step in
solving any equation that contains grouping symbols.
Example
Solve each equation. Check your
solution.
1. 8 = 4(3x
+ 5)
Alternative Solutions :
8 = 4(3x + 5) Original
equation
8 = 12x + 20 Distributive Property
8 – 20 = 12x +
20 – 20 Subtract
20 from each side.
–12 = 12x Simplify.
Divide
each side by 12.
–1 = x Simplify.
Check:
8 = 4(3x + 5) Original equation
8 ≟ 4[3(–1) 5] Replace
x with –1.
8 ≟ 4(–3 + 5) Multiply.
8 ≟ 4(2) Add.
8 = 8 ü Multiply.
2. 2(3n
– 5) – 3(1 – n) = 5
Alternative Solutions :
2(3n – 5) – 3(1 – n) = 5 Original equation
6n – 10 – 3 + 3n = 5 Distributive Property
9n – 13 = 5 Add
like terms.
9n – 13 + 13 =
5 + 13 Add
13 to each side.
9n = 18 Simplify.
Divide each side by 9.
n = 2 Simplify.
Check:
2(3n – 5) – 3(1 – n) = 5 Original equation
2[3(2) – 5) – 3(1 – 2)] ≟ 5 Replace n with 2.
2(6 – 5) – 3(–1) ≟ 5 Simplify.
2(1) + 3 ≟ 5 Simplify.
5 = 5 ü
Example
Building Link
3. The
Rock and Roll Hall of Fame in Cleveland, Ohio, has a trapezoidshaped cinema
with an area of about 4675 square feet. Find x, the approximate width of the movie screen in the cinema.
Alternative
Solutions :
The width
of the movie screen is 55 feet.
Sumber
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