18 questions were answered correctly.
2 questions were answered incorrectly.
1
Find the solution for x if |6x +
... [Show More] 8|=32.
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•
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correct
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RATIONALE
To solve this equation, we will need to create two
separate equations without absolute value bars.
One equation will contain the expression exactly as it
appears within the absolute value bars. The second
equation must consider the case when the expression
has the opposite value. Next, solve each equation
separately, starting with 6x + 8=32.
To solve for x, start by subtracting 8 from both sides.
CONCEPT
Absolute Value Equations
2
Suppose that 3y – 5 = 45 and y = 3x – 2.
Which of the following equations is equivalent to 3y – 5 = 45, but
written only in terms of x?
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9x – 6 = 50 correct
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9x – 6 = 40
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15x – 10 = 40
On the left, we have only 6x. On the right 32 minus 8 is
24. Then divide both sides by 6 to isolate x.
The solution for the first equation is x = 4. The same
process can be applied to the second equation 6x + 8 =
-32.
To solve, start by subtracting 8 from both sides.
On the left, we have only 6x. On the right -32 minus 8 is
-40. Then divide both sides by 6 to isolate x.
The solution for the second equation is .
The two solutions to |6x + 8| = 32 are x = 4 and
.
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15x – 10 = 50
RATIONALE
CONCEPT
Substitution in multi-step linear equations
3
Jacob opened a money-market account. In the first month,
he made an initial deposit of $500, and he plans to contribute an
additional $75 every month. The account does not pay any
interest.
After how many months will he have a total of $1,475?
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12 months
To find an equivalent equation written in terms of x we
can use the second equation y = 3x – 2. This equation
indicates that y is equivalent to 3x – 2 so we can
substitute 3x – 2 in for y in the first equation 3y – 5 = 45.
Now we have an equation in terms of x. To simplify it, first
apply the Distributive Property and multiply 3 by the
terms in the parentheses.
3 times 3x equals 9x, and 3 times -2 equals -6. Next,
eliminate -5 from the left side of the equation by adding
5 to both sides.
45 plus 5 equals 50. This equation is equivalent to the
original equation, but is written in terms of x.
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15 months
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13 months
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14 months correct
RATIONALE
Once each known value is substituted, we can solve
for n. First, distribute 75 into (n – 1).
75(n – 1) is equivalent to 75n – 75. Next, combine like
terms on the right side.
500 minus 75 is equal to 425. Subtract this value from
both sides to isolate the n term.
1475 minus 425 equals 1050. Finally divide both sides
by 75.
1050 divided by 75 is equal to 14. It will take 14
months for the balance to reach $1,475. [Show Less]