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SAT Math : Equations / Inequalities

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Example Questions

Example Question #5 : Solution Sets

Using the ordered pairs listed below, which of the following equations is true?

(0, –4)

(2, 0)

(4, 12)

(8, 60)

Possible Answers:

$y=x^{2}+4$

$y=x^{2}-4$

$y=2x^{2}+8$

$y=2x^{2}-8$

Correct answer:

$y=x^{2}-4$

Explanation:

You can solve this problem using the guess and check method by substituting the first number in the ordered pair for "x" and the second number for "y". Therfore the correct answer is $y=x^{2}-4$

–4 = 0 – 4

0 = 4 – 4

12 = 16 – 4

60 = 64 – 4

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Example Question #2 : Solution Sets

Solve for x: $(x-8)^{2}=36$

Possible Answers:

x = –2 or –14

x = 14

x = 14 or 2

x = 14 or –2

x = 2 or –14

Correct answer:

x = 14 or 2

Explanation:

First, take the square root of both sides:

$x-8=\pm 6$

Therefore, $x-8=6$ or $x-8 = -6$

Add 8 to both sides of the equation; therefore, $x=14$ or $x=2$

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Example Question #2 : How To Find A Solution Set

What is a possible solution to this equation: $y= x^{2}+3x-2$ ?

Possible Answers:

(3, 16)

(2, 6)

(3, 18)

There is no solution.

(2, 10)

Correct answer:

(3, 16)

Explanation:

This equation can be solved using the guess and check method.

$3^{2}+(3\times 3)-2= 9+9-2=16$

Therefore, the ordered pair (3, 16) is the correct answer.

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Example Question #8 : Solution Sets

$0.1(x-5)+0.03(2x+5)=0.5(x)$

Possible Answers:

$34$

$-35$

$-\frac{35}{34}$

$-34$

$35$

Correct answer:

$-\frac{35}{34}$

Explanation:

First multiply each decimal number in each term by 100 to remove the decimals (to get a whole number you have to multiply 0.03 by 100 to get 3). You need to do this for terms on both sides of the equal sign.

The second method would be to look for the number of digits to the right of the decimal point (e.g., 0.03 has two digits). So in this method shift the decimal point to the right two places.

Now the equation looks as follows:

$10x-50+6x+15=50x$

Now solve for $x$ and $x$ will be equal to $-\frac{35}{34}$ .

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Example Question #9 : Solution Sets

Solve $|z-2|\leq 0$

Possible Answers:

$z<0$

$z=2$

$z>0$

$All\ real\ numbers$

$No\ solutions$

Correct answer:

$z=2$

Explanation:

Absolute value is the distance from the point to the origin, so the value itself is always poisitive. The only solution that makes sense for this problem is when the absolute value is equal to zero, or $z-2=0$ and that happens when $z=2$ .

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Example Question #171 : Equations / Inequalities

In this question we describe the solution set in the form of a line diagram. Remember a solution to an inequality can be described in the form of (1) Inequality notation, (2) A line diagram, (3) and or an interval notation.

Given a solution set for a linear inequality as shown below:

$\left \{ x|x<-2 \ or\ x>3 \right \}$

what would be the correct representation of the above set in the form of a line diagram

Possible Answers:

Correct answer:

Explanation:

The solution lies in the set of real numbers less than $-2$ or the set of real numbers greater than $3$ .

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Example Question #172 : Equations / Inequalities

Solve and describe your answer in both inequality notation and interval notation:

$10< -3a+10\leq 34$

Possible Answers:

$-8 \leq a< 0$

$\left [ -8,0\left \right )$

$\left ( 0, -8]$

$\left ( 8,0 \right )$

$-a \leq -8$

$-8\leq a> 0$

Correct answer:

$-8 \leq a< 0$

$\left [ -8,0\left \right )$

Explanation:

This is a question with double inequality.

First solve the left side which will be $10< -3a+10$ which will give you $a<0$ and then solve the right side which is $-3a+10\leq 34$ and solution is $-a\leq 8$ which is really equal to $a\geq -8$

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Example Question #12 : How To Find A Solution Set

$\left | 2x-3 \right |\leq 5$

Possible Answers:

$x\leq 4$

$x\leq 4 , x\geq -1$ OR $\left [ -1,4 \right ]$

$\left [ 4,-\alpha \)\cup \left [ -1, +\alpha \ )$

$x\geq -1$

Correct answer:

$x\leq 4 , x\geq -1$ OR $\left [ -1,4 \right ]$

Explanation:

This question deals with absolute value inequalities and as a result you get a set of solutions.

The first solution involves solving $2x - 3\leq 5$ which gives you $x\leq 4$ .

Next solve for $2x-3\geq -5$ which will give you $x\geq -1$ .

Since $x\leq 4$ and $x\geq -1$ overlap, the correct solution is [-1,4]

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Example Question #11 : Solution Sets

$.63475634...$ : What is the 22nd digit after the decimal?

Possible Answers:

$4$

$3$

$6$

$5$

$7$

Correct answer:

$3$

Explanation:

The repeating pattern after the decimal is 63475, so the 22nd number would be 3.

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Example Question #12 : Solution Sets

$\left | x+3 \right |\leq -4$

Possible Answers:

$x\leq -7, x\geq +1$

$No\ solution$

$None\ of\ the\ answers.$

$x\geq 1$

$x\leq -7$

Correct answer:

$No\ solution$

Explanation:

This problem deals with absolute value inequalities.

An absolute value expression can never be less than 0. So the correct answer is "No Solution"

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SAT Math : Equations / Inequalities

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #5 : Solution Sets

Example Question #2 : Solution Sets

Example Question #2 : How To Find A Solution Set

Example Question #8 : Solution Sets

Example Question #9 : Solution Sets

Example Question #171 : Equations / Inequalities

Example Question #172 : Equations / Inequalities

Example Question #12 : How To Find A Solution Set

Example Question #11 : Solution Sets

Example Question #12 : Solution Sets

All SAT Math Resources

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