Answer:
1a) divide both sides by 2
1b) multiply both sides by -1
2a) 2x+4
2b) 2x
2c) P = 2x+4; A = 2x
Step-by-step explanation:
To solve equations, you take advantage of the properties of equality and of identity elements.
The multiplicative identity element is 1. (Multiplying by 1 does not change the value of a number or expression.) The product of a number and its reciprocal is the multiplicative identity element.
The multiplication property of equality tells you that you can multiply both sides of an equation by the same value, and the value of the variable remains the same. (The equal sign remains true.)
Of course, division by 'a' is the same as multiplication by 1/a.
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1a) We have 2x on the left. We want 1x on the left. The properties discussed above say we can multiply both sides of the equation by the multiplicative inverse of 2 and the result will be what we're after.
(1/2)(2x) = (1/2)(17) . . . . multiply both sides by 1/2 (equivalently, divide by 2)
x = 17/2
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1b) The coefficient of x is -1. The reciprocal of that is also -1. So, we can multiply this equation by -1 to get what we're after.
(-1)(-x) = (-1)(9) . . . . multiply both sides by -1
x = -9
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2a) The perimeter is the sum of the lengths of all the sides. Opposite sides of a rectangle have the same length. So, the perimeter is ...
2 + x + 2 + x = 2x+4 . . . . . . listing sides CW from the top
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2b) The area is the product of the side lengths:
(x)(2) = 2x
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2c) As equations, we can write perimeter (P) and area (A) as ...
P = 2x+4
A = 2x
