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PSAT Math : How to evaluate algebraic expressions

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Example Question #41 : How To Evaluate Algebraic Expressions

The function $\small f(x)$ is given as $\small f(x)=21-5x$ . If $\small \small f(a+2)=4$ , what is the value of $\small a$ ?

Possible Answers:

$\small \frac{17}{5}$

$\small \frac{7}{5}$

$\small -\frac{17}{5}$

$\small -\frac{7}{5}$

$\small 5$

Correct answer:

$\small \frac{7}{5}$

Explanation:

This is a simple substitution problem. Begin by setting the function $\small f(x)$ equal to $\small 4$ :

$\small 21-5x = 4$

Solve for $\small x$ :

$\small 21-5x-21=4-21$

$\small -5x = -17$

$\small \frac{-5x}{-5}=\frac{-17}{-5}$

$\small x=\frac{17}{5}$

A common mistake at this point is to believe that you have finished the question. We are given that $\small f(a+2) = 4$ . We must now substitute $\small a+2$ for $\small x$ and solve for $\small a$ :

$\small x=\frac{17}{5}$

$\small a+2 = \frac{17}{5}$

Subtract 2 from both sides:

$\small a+2-2 = \frac{17}{5}-2$

$\small a = \frac{17}{5}-\frac{10}{5}$

$\small a = \frac{7}{5}$

The answer is $\small \frac{7}{5}$ .

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Example Question #421 : Algebra

Which of the following numbers is eight more than half of itself?

Possible Answers:

Correct answer:

Explanation:

Word problems like this are a common occurrence on the PSAT. Begin by setting the number we are looking for, let's call it $\small x$ , equivalent to the equation we are given in the words.

$\small x = \frac{1}{2}x+8$

Move all terms with the variable to one side:

$\small x-\frac{1}{2}x=\frac{1}{2}x+8-\frac{1}{2}x$

$\small \frac{1}{2}x = 8$

Multiply both sides by 2:

$\small x=16$

The correct answer is 16.

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Example Question #41 : Expressions

Fahrenheit temperature can be converted to its Celsius equivalent using the formula

$C = \frac{5}{9} (F-32)$ .

Celsius temperature can be converted to its Fahrenheit equivalent using the formula

$F = \frac{9}{5} C + 32$ .

Mercury boils at $357 ^{\circ } C$ . To the nearest degree, convert this to its equivalent Fahrenheit temperature.

Possible Answers:

$166^{\circ } F$

$675^{\circ } F$

$700^{\circ } F$

None of the other responses is correct.

$181^{\circ } F$

Correct answer:

$675^{\circ } F$

Explanation:

The formula to use is

$F = \frac{9}{5} C + 32$ .

Substitute 357 for :

$F = \frac{9}{5} (357) + 32 = 642.6 + 32 = 674.6$

To the nearest degree, this is $675^{\circ } F$ .

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PSAT Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #41 : How To Evaluate Algebraic Expressions

Example Question #421 : Algebra

Example Question #41 : Expressions

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