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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #4 : Inequalities

If 2 more than is a negative integer and if 5 more than is a positive integer, which of the following could be the value of ?

Possible Answers:

-7

Correct answer:

Explanation:

m+2 < 0 and m+5 > 0 , so m < -2 and m > -5 . The only integers between and are and .

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Example Question #4 : Inequalities

If $\frac{a}{5}+5> 6$ , which of the following MUST be true?

I. $a> 2$

II. $a> 10$

III. $a< 6$

Possible Answers:

I, II, and III

III only

I and II only

II only

I only

Correct answer:

I only

Explanation:

Subtract 5 from both sides of the inequality:

$\frac{a}{5}> 1$

Multiply both sides by 5:

$a> 5$

Therefore only I must be true.

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Example Question #5 : Inequalities

Which of the following is equivalent to $\left | x-3 \right |<2$ ?

Possible Answers:

-3 < x < 2

x>-1

1 < x < 5

x>1

x<5

Correct answer:

1 < x < 5

Explanation:

Solve for both x – 3 < 2 and –(x – 3) < 2.

x – 3 < 2 and –x + 3 < 2

x < 2 + 3 and –x < 2 – 3

x < 5 and –x < –1

x < 5 and x > 1

The results are x < 5 and x > 1.

Combine the two inequalities to get 1 < x < 5

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Example Question #6 : Inequalities

Given $\left | 7x+9\right |>30$ , what is a possible value of ?

Possible Answers:

$-\frac{39}{7}$

Correct answer:

Explanation:

In order to find the range of possible values for $\left | 7x+9\right |>30$ , we must first consider that the absolute value applied to this inequality results in two separate equations, both of which we must solve:

7x+9>30 and 7x+9< -30 .

Starting with the first inequality:

7x+9>30

7x>21

x>3

Then, our second inequality tells us that

7x+9< -30

7x< -39

$x<-\frac{39}{7}(or -5\frac{4}{7})$

Therefore, is the correct answer, as it is the only value above for which x>3 (NOT greater than or equal to) or $x<-\frac{39}{7}$ (NOT less than or equal to).

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Example Question #5 : Inequalities

The cost, in cents, of manufacturing $\dpi{100} \small x$ pencils is $\dpi{100} \small 1200+20x$ , where 1200 is the number of cents required to run the factory regardless of the number of pencils made, and 20 represents the per-unit cost, in cents, of making each pencil. The pencils sell for 50 cents each. What number of pencils would need to be sold so that the revenue received is at least equal to the manufacturing cost?

Possible Answers:

$\dpi{100} \small 40$

$\dpi{100} \small 36$

$\dpi{100} \small 33$

$\dpi{100} \small 27$

$\dpi{100} \small 30$

Correct answer:

$\dpi{100} \small 40$

Explanation:

If each pencil sells at 50 cents, $\dpi{100} \small x$ pencils will sell at $\dpi{100} \small 50x$ . The smallest value of $\dpi{100} \small x$ such that

$\dpi{100} \small 50x\geq 1200+20x$

$\dpi{100} \small x\geq 40$

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Example Question #5 : Inequalities

Solve for :

-3x+5<101

Possible Answers:

x<-32

x>-32

x>32

x<32

x=32

Correct answer:

x>-32

Explanation:

The correct method to solve this problem is to substract 5 from both sides. This gives -3x<96 .

Then divide both sides by negative 3. When dividing by a negative it is important to remember to change the inequality sign. In this case the sign goes from a less than to a greater than sign.

This gives the answer x>-32 .

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Example Question #1 : Inequalities

$\dpi{100} \small -2y+7>-7+y$

Given the inequality above, which of the following MUST be true?

Possible Answers:

$\dpi{100} \small y<\frac{-14}{3}$

$\dpi{100} \small y>\frac{-14}{3}$ $y>\textup{2}$

$\dpi{100} \small y<5$ $y< \textup{3}$

$\dpi{100} \small y>\frac{14}{3}$

$\dpi{100} \small y>-5$ $y < \textup{5}$

Correct answer:

$\dpi{100} \small y>-5$ $y < \textup{5}$

Explanation:

$\dpi{100} \small -2y+7>-7+y$ Subtract from both sides:

-2y+7-y>-7+y-y

-3y+7>-7

Subtract 7 from both sides:

-3y+7-7>-7-7

-3y>-14

Divide both sides by $\dpi{100} \small -3$ :

$\frac{-3y}{-3}>\frac{-14}{-3}$

Remember to switch the inequality when dividing by a negative number:

$y<\frac{14}{3}$

Since $\dpi{100} \small y<\frac{14}{3}$ is not an answer, we must find an answer that, at the very least, does not contradict the fact that is less than (approximately) 4.67. Since any number that is less than 4.67 is also less than any number that is bigger than 4.67, we can be sure that is less than 5.

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Example Question #2 : Inequalities

A factory packs cereal boxes. Before sealing each box, a machine weighs it to ensure that it is no lighter than 356 grams and no heavier than 364 grams. If the box holds grams of cereal, which inequality represents all allowable values of ?

Possible Answers:

$\left | w+360 \right |<4$

$\left | w-360 \right |>4$

$\left | w-360 \right |=4$

$\left | w-360 \right |\leq4$

$\left | w+360 \right |\geq4$

Correct answer:

$\left | w-360 \right |\leq4$

Explanation:

The median weight of a box of cereal is 360 grams. This should be an allowable value of w. Substituting 360 for w into each answer choice, the only true results are:

$\\ |w -360| \leq 4 \\ |360 -360| \leq 4 \\0 \leq 4$

and:

$\\|w + 360| \geq 4 \\ |360 + 360| \geq 4\\ 720 \geq4$

Notice that any positive value for w satisfies the second inequality above. Since w must be between 356 and 364, the first inequality above is the only reasonable choice.

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Example Question #11 : How To Find The Solution To An Inequality With Subtraction

Solve for .

$4x-8\geq 28$

Possible Answers:

x<9

x>9

x=9

$x\leq 9$

$x\geq 9$

Correct answer:

$x\geq 9$

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

$4x-8\geq 28$ Add on both sides.

$4x\geq 36$ Divide on both sides.

$x\geq 9$

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Example Question #13 : Inequalities

Solve for .

-9x-38>25

Possible Answers:

x>-7

x<-7

$x\geq -7$

$x\leq -7$

x=-7

Correct answer:

x<-7

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

-9x-38>25 Add on both sides.

-9x>63 Divide on both sides. Remember to flip the sign.

x<-7

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #4 : Inequalities

Example Question #4 : Inequalities

Example Question #5 : Inequalities

Example Question #6 : Inequalities

Example Question #5 : Inequalities

Example Question #5 : Inequalities

Example Question #1 : Inequalities

Example Question #2 : Inequalities

Example Question #11 : How To Find The Solution To An Inequality With Subtraction

Example Question #13 : Inequalities

All SAT Math Resources

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