PSAT Math : Equations / Inequalities

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #11 : Inequalities

What values of x make the following statement true?

|x – 3| < 9

Possible Answers:

–3 < x < 9

6 < x < 12

–6 < x < 12

x < 12

–12 < x < 6

Correct answer:

–6 < x < 12

Explanation:

Solve the inequality by adding 3 to both sides to get x < 12.  Since it is absolute value, x – 3 > –9 must also be solved by adding 3 to both sides so: x > –6 so combined.

Example Question #1 : How To Find The Solution To An Inequality With Addition

If –1 < w < 1, all of the following must also be greater than –1 and less than 1 EXCEPT for which choice?

Possible Answers:

|w|

w2

3w/2

w/2

|w|0.5

Correct answer:

3w/2

Explanation:

3w/2 will become greater than 1 as soon as w is greater than two thirds. It will likewise become less than –1 as soon as w is less than negative two thirds. All the other options always return values between –1 and 1.

Example Question #191 : Equations / Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

Absolute value problems always have two sides: one positive and one negative.

First, take the problem as is and drop the absolute value signs for the positive side: z – 3 ≥ 5. When the original inequality is multiplied by –1 we get z – 3 ≤ –5.

Solve each inequality separately to get z ≤ –2 or z ≥ 8 (the inequality sign flips when multiplying or dividing by a negative number).

We can verify the solution by substituting in 0 for z to see if we get a true or false statement. Since –3 ≥ 5 is always false we know we want the two outside inequalities, rather than their intersection.

Example Question #21 : Inequalities

If x+1< 4 and y-2<-1 , then what is the value of ?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, add the two equations together:

x+1<4

y-2<-1

x+1+y-2<4-1

x+y-1<3

x+y<4

The only answer choice that satisfies this equation is 0, because 0 is less than 4.

Example Question #1 : How To Find The Solution To An Inequality With Addition

If , which of the following could be a value of ?

Possible Answers:

-

Correct answer:

Explanation:

In order to solve this inequality, you must isolate  on one side of the equation. 

Therefore, the only option that solves the inequality is

 

Example Question #22 : Inequalities

What values of  make the statement  true?

Possible Answers:

Correct answer:

Explanation:

First, solve the inequality :

Since we are dealing with absolute value,  must also be true; therefore:

Example Question #1 : How To Find The Solution To An Inequality With Multiplication

If –1 < n < 1, all of the following could be true EXCEPT:

Possible Answers:

16n2 - 1 = 0

(n-1)2 > n

n2 < 2n

n2 < n

|n2 - 1| > 1

Correct answer:

|n2 - 1| > 1

Explanation:

N_part_1

N_part_2

N_part_3

N_part_4

N_part_5

Example Question #11 : Inequalities

(√(8) / -x ) <  2. Which of the following values could be x?

Possible Answers:

-4

-3

All of the answers choices are valid.

-2

-1

Correct answer:

-1

Explanation:

The equation simplifies to x > -1.41. -1 is the answer.

Example Question #51 : New Sat Math Calculator

Solve for x

\small 3x+7 \geq -2x+4

 

Possible Answers:

\small x \geq -\frac{3}{5}

\small x \geq \frac{3}{5}

\small x \leq \frac{3}{5}

\small x \leq -\frac{3}{5}

Correct answer:

\small x \geq -\frac{3}{5}

Explanation:

\small 3x+7 \geq -2x+4

\small 3x \geq -2x-3

\small 5x \geq -3

\small x\geq -\frac{3}{5}

Example Question #5 : How To Find The Solution To An Inequality With Multiplication

We have , find the solution set for this inequality. 

Possible Answers:

Correct answer:

Explanation:

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