2019年SAT考试数学考前必练经典试题4

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Read the following SAT test question and then click on a button to select your answer.

4(x-2)+x=ax-8

If the equation has exactly one solution, which of the following could be the value of a?

I.3

II.5

A.NONE

B.I

C.II

D.I and II

答案：B

解析：

Choice B is correct. First, this is a linear equation ine one variable.

When a linear equation has one solution, the equation reduces to an equation of the form

ax+b=cx+d, where a does not equal c.

Rewrite the equation in an equivalent form using the distributive property and combining like terms

4(x-2)+x=ax-8

5x-8=ax-8

If a=5, the two sides of the equation are the same. In this case, there are infinitely many solutions.

If a is any number other than 5, the equation will have exactly one solution, x=0. In this case, the only correct answer is a=3.

If a=3, the equation will have exactly one solution.

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