SAT Linear Equations in One Variable Question 40 | Free SAT Prep | Aniko

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Question 40·Easy·Linear Equations in One Variable

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4(2 - m) = 20

What is the value of $m$ ?

Your answer

(Express the answer as an integer)

For linear equations with parentheses, first distribute any numbers multiplying the parentheses to remove them. Then collect like terms so that all variable terms are on one side and constants on the other. Use inverse operations in a clear order—add/subtract to move constants, then multiply/divide to isolate the variable—being especially careful with negative signs to avoid common errors.

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Remove the parentheses

First, think about how to get rid of the parentheses in $4(2 - m)$ . What should you do with the 4?

Simplify to a linear equation

After distributing the 4, you should get an equation of the form $a + bm = 20$ . What does that equation look like?

Isolate the variable

Once you have something like $8 - 4m = 20$ , move the constant (the number without $m$ ) to the other side, then divide to solve for $m$ .

Desmos Guide

Enter each side as a separate function

In Desmos, in the first line type y = 4(2 - x) and in the second line type y = 20. Here, $x$ plays the role of $m$ .

Find the intersection point

Look for the point where the two graphs intersect. Click on the intersection; the $x$ -coordinate of this point is the value of $m$ that makes $4(2 - m) = 20$ true.

Step-by-step Explanation

Distribute the 4

Start by multiplying 4 by each term inside the parentheses:

4(2 - m) = 20 \Rightarrow 8 - 4m = 20

Now you have a simpler linear equation without parentheses.

Isolate the term with m

Move the constant term 8 to the right side by subtracting 8 from both sides:

\begin{aligned} 8 - 4m &= 20 \\ -4m &= 20 - 8 \\ -4m &= 12 \end{aligned}

Now the equation has only the $m$ term on the left side.

Solve for m

Divide both sides of the equation by $-4$ to solve for $m$ :

\begin{aligned} -4m &= 12 \\ m &= \frac{12}{-4} = -3 \end{aligned}

So, the value of $m$ is $-3$ .

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation