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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #224 : New Sat

Solve

$\frac{4x-4}{x+4}=10$

Possible Answers:

x=-22

$x=-\frac{22}{3}$

x=-3

$x=\frac{22}{3}$

Correct answer:

$x=-\frac{22}{3}$

Explanation:

$\frac{4x-4}{x+4}=10$

First multiply by the denominator on each side

$\frac{4x-4}{x+4}\cdot(x+4)=10(x+4)$

4x-4=10(x+4)

Expand left side, and solve for

4x-4=10x+40

-44=6x

$x=\frac{-44}{6}=-\frac{22}{3}$

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Example Question #103 : Algebra

Rational_5

Possible Answers:

–1

–2

Correct answer:

Explanation:

Rational_2

Rational_3

Rational_4

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Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Linesmb1

Possible Answers:

b/(m²+ 1)

–b/(m²– 1)

–b/(m + 1)

–bm/(m²+ 1)

bm/(m²+ 1)

Correct answer:

b/(m²+ 1)

Explanation:

Linesmb5

Linesmb4

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Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

In the equation below, , , and are non-zero numbers. What is the value of in terms of and ?

$\frac{1}{m^3}-\frac{1}{k^2}=\frac{1}{p}$

Possible Answers:

$m=(\frac{p+k^2}{pk^2})^{\frac{1}{3}}$

$m=\frac{p^2k^3}{p+k^2}$

$m=(\frac{p+k^2}{2})^3$

$m=p^{\frac{1}{2}}-k^{\frac{1}{3}}$

$m=(\frac{pk^2}{p+k^2})^{\frac{1}{3}}$

Correct answer:

$m=(\frac{pk^2}{p+k^2})^{\frac{1}{3}}$

Explanation:

Pkm_7-21-13

Pkm2_7-21-13

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Example Question #106 : Algebra

Solve for x:

$\frac{x+3}{7}=3$

Possible Answers:

x=42

x=0

x=18

x=24

x=6

Correct answer:

x=18

Explanation:

The first step is to cancel out the denominator by multiplying both sides by 7:

$7\cdot \frac{x+3}{7}=3\cdot7$

x+3=21

Subtract 3 from both sides to get by itself:

x+3-3=21-3

x=18

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Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

Solve for and using elimination:

2x+3y=5

-x-2y=-8

Possible Answers:

x=-14 and y=11

x=-8 and y=-4

x=8 and y=4

$x=\frac{5}{2}$ and $y=\frac{5}{3}$

x=14 and y=-11

Correct answer:

x=-14 and y=11

Explanation:

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 :

2x+3y=5

2(-x-2y)=2(-8)

Now our two equations look like this:

2x+3y=5

-2x-4y=-16

The can cancel with the -2x , giving us:

3y=5

-4y=-16

These equations, when summed, give us:

-y=-11

y=11

Once we know the value for , we can just plug it into one of our original equations to solve for the value of :

2x+3y=5

2x+3(11)=5

2x+33=5

2x=-28

x=-14

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Example Question #111 : Algebra

Give the solution set of the rational equation $\frac{(x- 5)^{2}}{(x- 4) ^{2}} = 1$

Possible Answers:

$\left \{ - \frac{1}{2}, \frac{9}{2} \right \}$

$\left \{ \frac{9}{2} \right \}$

$\left \{ 5\right \}$

$\left \{ - \frac{9}{2}, \frac{9}{2} \right \}$

$\left \{ 4, 5\right \}$

Correct answer:

$\left \{ \frac{9}{2} \right \}$

Explanation:

Multiply both sides of the equation by the denominator $(x- 4) ^{2}$ :

$\frac{(x- 5)^{2}}{(x- 4) ^{2}} \cdot (x- 4) ^{2} =1 \cdot (x- 4) ^{2}$

$(x- 5)^{2} = (x- 4) ^{2}$

Rewrite both expression using the binomial square pattern:

$x^{2} - 2 \cdot x \cdot 5+ 5^{2} = x^{2} - 2 \cdot x \cdot 4+ 4^{2}$

$x^{2} -10x + 25 = x^{2} - 8x+16$

This can be rewritten as a linear equation by subtracting $x^{2}$ from both sides:

$x^{2} -10x + 25- x^{2} = x^{2} - 8x+16 - x^{2}$

-10x + 25 = - 8x+16

Solve as a linear equation:

-10x + 25+ 8x - 25 = - 8x+16 + 8x - 25

-2x = -9

$\frac{-2x}{-2 } =\frac{ -9 }{-2}$

$x= \frac{9}{2}$

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Example Question #3 : How To Find The Solution To A Rational Equation With Lcd

Solve:

$\frac{10-x}{40}=-5$

Possible Answers:

x=-200

x=-210

x=210

x=200

x=21

Correct answer:

x=210

Explanation:

$\frac{10-x}{40}=-5$

Multiply by on each side

10-x=-200

Subtract on each side

-x=-210

Multiply by on each side

x=210

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Example Question #2 : How To Find Out When An Equation Has No Solution

Find the solution to the following equation if x = 3:

y = (4x² - 2)/(9 - x²)

Possible Answers:

no possible solution

Correct answer:

no possible solution

Explanation:

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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Example Question #4 : How To Find Out When An Equation Has No Solution

Undefined_denom3

I. x = 0

II. x = –1

III. x = 1

Possible Answers:

II only

II and III only

I, II, and III

III only

I only

Correct answer:

I only

Explanation:

Undefined_denom2

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #224 : New Sat

Example Question #103 : Algebra

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

Example Question #106 : Algebra

Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

Example Question #111 : Algebra

Example Question #3 : How To Find The Solution To A Rational Equation With Lcd

Example Question #2 : How To Find Out When An Equation Has No Solution

Example Question #4 : How To Find Out When An Equation Has No Solution

All SAT Math Resources

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