PSAT Math Practice Questions: Linear Equations

Linear equations and linear graphs are some of the most common test questions on the PSAT Math Test. Linear Equations can be used to model relationships and changes such as those concerning time, temperature, or population. The graphs of these equations are as important as the equations themselves. Let’s review an example.

PSAT Math Practice Question: Linear Equations

Work through the Kaplan Method for Math step-by-step to solve the following question. The table below shows Kaplan’s strategic thinking on the left, along with suggested math scratchwork on the right.

$\frac{8}{7}\left(x-\frac{101}{220}\right)+4\left(x+\frac{8}{9}\right)=38$

Which approximate value of x satisfies the equation shown?

A) 4.29

B) 4.65

C) 6.6

D) 6.8

Strategic Thinking Math Scratchwork

Step 1: Read the question, identifying and organizing important information as you go

Notice a pattern? Again, the question is asking you to solve for x.

$\frac{8}{7}\left(x-\frac{101}{220}\right)+4\left(x+\frac{8}{9}\right)=38$

Step 2: Choose the best strategy to answer the question

How can you quickly solve this problem?

Clearing the fraction outside the parentheses is a smart move. Multiply both sides by 7.

What do you notice about the answer choices? How are they different from the answers in the last problem?

The presence of decimals means your calculator will be a great asset here. Don’t worry about common denominators. Divide the fractions. Because the answer choices are only written to two decimal places, write your intermediate steps to two places as well.

Now distribute the numbers outside the parentheses, collect like terms, and solve for x

$8\left(x-\frac{101}{220}\right)+28\left(x+\frac{8}{9}\right)=266$

8(x - 0.46) + 28(x + 0.89) = 266

8x - 3.68 + 28x + 24.92 = 266

36x = 244.76

x = 6.8

Step 3: Check that you answered the right question

Double-check the question stem. Choice (D) is correct.

x = 6.8

Many graphing calculators have a built-in function that will let you input and solve algebraic equations like the previous one. Consider learning how to use it before Test Day by reading the instruction manual or searching online. Notice in the previous question that careful use of your calculator can eliminate the need to complete time-consuming tasks by hand. Be conscious of the format of the answer choices—decimal answers are a great clue that you can use your calculator.

Laura AitchesonKaplan PSAT Expert

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