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Linear equations in one variable — SAT practice questions

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Practice 134 Linear equations in one variable questions in the app

What this topic is

Linear equations in one variable on the SAT Math section cover solving equations that reduce to a single unknown of degree one, including word problems and equations with a parameter.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

A 40-liter mixture is $20\%$ acid. How many liters of a $50\%$ acid solution must be added to make the resulting mixture $30\%$ acid?

A10✗ Not this oneB16✗ Not this oneC20✓ CorrectD24✗ Not this one

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Answer: C — 20

If $x$ liters are added, then $0.20(40)+0.50x=0.30(40+x)$. This gives $8+0.5x=12+0.3x$, so $x=20$.

Question 2Easier

If $12x-27=45$, what is the value of $4x-9$?

A9✗ Not this oneB15✓ CorrectC18✗ Not this oneD45✗ Not this one

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Answer: B — 15

Notice that $4x-9=\dfrac{1}{3}(12x-27)$. Since $12x-27=45$, we get $4x-9=\dfrac{45}{3}=15$.

Question 3Easier

$r(5x-2)+8x=38x-12$

In the given equation, $r$ is a constant. The equation has infinitely many solutions. What is the value of $r$?

A$-6$✗ Not this oneB6✓ CorrectC$\dfrac{46}{5}$✗ Not this oneD12✗ Not this one

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Answer: B — 6

Expanding the left side gives $(5r+8)x-2r$. Matching both sides requires $5r+8=38$ and $-2r=-12$, and both conditions give $r=6$.

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