9514 1404 393
Answer:
a. x = 13/7
b. j = 3
c. y = 2
d. p = 25
Explanation:
Here, it is convenient to combine like terms first. When you do that, you see that one side of the equation has a mix of a constant term and a variable term. Choose the term that matches the kind of term present on the other side of the equation (constant or variable), then add its opposite to both sides. Finally, divide by the coefficient of the variable.
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a. 3x +13 = 10x . . . . combine like terms
13 = 7x . . . . . . . . . subtract 3x
13/7 = x . . . . . . . . divide by the coefficient of x
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b. 10j -20 = 10 . . . . combine like terms
10j = 30 . . . . . . . . add 20
j = 3 . . . . . . . . . . . divide by 10
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c. 6y = 14 -y . . . . . . combine like terms
7y = 14 . . . . . . . . . add y
y = 2 . . . . . . . . . . divide by 7
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d. p + 8 = 33 . . . . . . combine like terms
p = 25 . . . . . . . . . add -8
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Comment on solving equations
In these "2-step" equations, the first step (after simplifying, combining like terms) is to "separate the variable and constant terms". The basic idea is to determine what term you don't want where it is, then add its opposite to both sides of the equation.
You can do anything you like to the equation, provided you do the same thing to both sides. When we say "subtract 3x," for example, we mean 3x is subtracted from both sides of the equation. This is an example of the use of the addition property of equality.
The same goes for multiplication or division. You can multiply or divide by anything you like, as long as you do the same thing to both sides of the equation. In the above, "divide by 7," for example, means both sides of the equation are divided by 7.