Linear / Rational / Variable Equations - SAT Math
Card 0 of 960
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In the equation below, 
, 
, and 
are non-zero numbers. What is the value of 
in terms of 
and 
?
In the equation below,
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Solve for x:
Solve for x:
The first step is to cancel out the denominator by multiplying both sides by 7:
Subtract 3 from both sides to get 
by itself:
The first step is to cancel out the denominator by multiplying both sides by 7:
Subtract 3 from both sides to get
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Solve for 
and 
using elimination:
Solve for
When using elimination, you need two factors to cancel out when the two equations are added together. We can get the 
in the first equation to cancel out with the 
in the second equation by multiplying everything in the second equation by 
:
Now our two equations look like this:
The 
can cancel with the 
, giving us:
These equations, when summed, give us:
Once we know the value for 
, we can just plug it into one of our original equations to solve for the value of 
:
When using elimination, you need two factors to cancel out when the two equations are added together. We can get the
Now our two equations look like this:
The
These equations, when summed, give us:
Once we know the value for
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Give the solution set of the rational equation 
Give the solution set of the rational equation
Multiply both sides of the equation by the denominator 
:
Rewrite both expression using the binomial square pattern:
This can be rewritten as a linear equation by subtracting 
from both sides:
Solve as a linear equation:
Multiply both sides of the equation by the denominator
Rewrite both expression using the binomial square pattern:
This can be rewritten as a linear equation by subtracting
Solve as a linear equation:
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Solve:
Solve:
Multiply by 
on each side
Subtract 
on each side
Multiply by 
on each side
Multiply by
Subtract
Multiply by
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Find the solution to the following equation if x = 3:
y = (4x2 - 2)/(9 - x2)
Find the solution to the following equation if x = 3:
y = (4x2 - 2)/(9 - x2)
Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.
Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.
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I. x = 0
II. x = –1
III. x = 1
I. x = 0
II. x = –1
III. x = 1
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A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.
A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.
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Solve:
Solve:
First, distribute, making sure to watch for negatives.
Combine like terms.
Subtract 7x from both sides.
Add 18 on both sides and be careful adding integers.
First, distribute, making sure to watch for negatives.
Combine like terms.
Subtract 7x from both sides.
Add 18 on both sides and be careful adding integers.
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Solve:
Solve:
First, distribute the 
to the terms inside the parentheses.
Add 6x to both sides.
This is false for any value of 
. Thus, there is no solution.
First, distribute the
Add 6x to both sides.
This is false for any value of
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Solve 
.
Solve
By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.
By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.
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, 
In the above graphic, approximately determine the x values where the graph is neither increasing or decreasing.
,
In the above graphic, approximately determine the x values where the graph is neither increasing or decreasing.
We need to find where the graph's slope is approximately zero. There is a straight line between the x values of 
, and 
. The other x values have a slope. So our final answer is 
.
We need to find where the graph's slope is approximately zero. There is a straight line between the x values of
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If 4_xs = v, v = ks , and sv ≠_ 0, which of the following is equal to k ?
If 4_xs = v, v = ks , and sv ≠_ 0, which of the following is equal to k ?
This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4_xs and ks are both equal to v, which means that 4_xs_ and ks must be equal to each other--that is, 4_xs_ = ks. Dividing both sides by s gives 4_x_ = k, which is our solution.
This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4_xs and ks are both equal to v, which means that 4_xs_ and ks must be equal to each other--that is, 4_xs_ = ks. Dividing both sides by s gives 4_x_ = k, which is our solution.
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Solve for z:
3(z + 4)3 – 7 = 17
Solve for z:
3(z + 4)3 – 7 = 17
1. Add 7 to both sides
3(z + 4)3 – 7 + 7= 17 + 7
3(z + 4)3 = 24
2. Divide both sides by 3
(z + 4)3 = 8
3. Take the cube root of both sides
z + 4 = 2
4. Subtract 4 from both sides
z = –2
1. Add 7 to both sides
3(z + 4)3 – 7 + 7= 17 + 7
3(z + 4)3 = 24
2. Divide both sides by 3
(z + 4)3 = 8
3. Take the cube root of both sides
z + 4 = 2
4. Subtract 4 from both sides
z = –2
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If 11 + 3_x_ is 29, what is 2_x_?
If 11 + 3_x_ is 29, what is 2_x_?
First, solve for x:
11 + 3_x_ = 29
29 – 11 = 3_x_
18 = 3_x_
x = 6
Then, solve for 2_x_:
2_x_ = 2 * 6 = 12
First, solve for x:
11 + 3_x_ = 29
29 – 11 = 3_x_
18 = 3_x_
x = 6
Then, solve for 2_x_:
2_x_ = 2 * 6 = 12
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If 2_x_ = 3_y_ = 6_z_ = 48, what is the value of x * y * z?
If 2_x_ = 3_y_ = 6_z_ = 48, what is the value of x * y * z?
Create 3 separate equations to solve for each variable separately.
-
2_x_ = 48
-
3_y_ = 48
-
6_z_ = 48
x = 24
y = 16
z = 8
x * y * z = 3072
Create 3 separate equations to solve for each variable separately.
-
2_x_ = 48
-
3_y_ = 48
-
6_z_ = 48
x = 24
y = 16
z = 8
x * y * z = 3072
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A sequence of numbers is: 2, 5, 8, 11. Assuming it follows the same pattern, what would be the value of the 20th number?
A sequence of numbers is: 2, 5, 8, 11. Assuming it follows the same pattern, what would be the value of the 20th number?
This goes up at a constant number between values, making it an arthmetic sequence. The first number is 2, with a difference of 3. Plugging this into the arithmetic equation you get An = 2 + 3 (n – 1). Plugging in 20 for n, you get a value of 59.
This goes up at a constant number between values, making it an arthmetic sequence. The first number is 2, with a difference of 3. Plugging this into the arithmetic equation you get An = 2 + 3 (n – 1). Plugging in 20 for n, you get a value of 59.
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