PSAT Math : Equations / Inequalities

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #71 : Equations / Inequalities

Solve for :

Possible Answers:

Correct answer:

Explanation:

Begin by moving all of the  values to the left side of the inequality:

becomes

Next, move the  to the right side:

Finally, divide both sides by :

Example Question #72 : Equations / Inequalities

Solve for :

Possible Answers:

Correct answer:

Explanation:

First, move the  values to the left side of the inequality:

becomes

Next, move the  to the right side:

Finally, divide by . Remember: you must flip the inequality sign when you multiply or divide by a negative number.

Example Question #73 : Equations / Inequalities

Solve for :

Possible Answers:

Correct answer:

Explanation:

First, get the  factors on the left side of the inequality:

becomes

Next, subtract  from both sides:

Now, divide by .  Remember: Dividing or multiplying by a negative number requires you to flip the inequality sign:

Example Question #74 : Equations / Inequalities

Solve the inequality

Possible Answers:

Correct answer:

Explanation:

First, multiplying each side of the equality by  gives . Next, dividing each side of the inequality by  will solve for .

Example Question #1937 : Sat Mathematics

What is the solution set of the inequality \dpi{100} \small 3x+8<35 ?

Possible Answers:

\dpi{100} \small x<35

\dpi{100} \small x>27

\dpi{100} \small x<9

\dpi{100} \small x<27

\dpi{100} \small x>9

Correct answer:

\dpi{100} \small x<9

Explanation:

We simplify this inequality similarly to how we would simplify an equation

\dpi{100} \small 3x+8-8<35-8

\dpi{100} \small \frac{3x}{3}<\frac{27}{3}

Thus \dpi{100} \small x<9

Example Question #1938 : Sat Mathematics

What is a solution set of the inequality ?

Possible Answers:

Correct answer:

Explanation:

In order to find the solution set, we solve  as we would an equation:

Therefore, the solution set is any value of .

Example Question #5 : 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

3

6

0

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.

Example Question #2 : Equations / Inequalities

Undefined_denom3

 

I.  x = 0

II. x = –1

III. x = 1

Possible Answers:

I only

I, II, and III

II and III only

III only

II only

Correct answer:

I only

Explanation:

 Undefined_denom2

Example Question #6 : How To Find Out When An Equation Has No Solution

Nosol1

Possible Answers:

–1/2

1

–3

There is no solution

3

Correct answer:

There is no solution

Explanation:

Nosol2

Example Question #7 : How To Find Out When An Equation Has No Solution

  

Possible Answers:

None of the other answers

Correct answer:

Explanation:

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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