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Linear and Quadratic Equations · Question 12 of 66

Question 12

HardOriginal question

The equation 3(x−a)=2x+53(x - a) = 2x + 5 has the solution x=2a−1x = 2a - 1. What is the value of aa?

Options for question 12

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. Substitute x=2a−1x = 2a - 1: 3(2a−1−a)=2(2a−1)+53(2a - 1 - a) = 2(2a - 1) + 5.

  2. Left side: 3(a−1)=3a−33(a - 1) = 3a - 3. Right side: 4a−2+5=4a+34a - 2 + 5 = 4a + 3.

  3. So 3a−3=4a+33a - 3 = 4a + 3, giving a=−6a = -6.

  4. Check: x=−13x = -13; 3(−13+6)=−213(-13 + 6) = -21 and 2(−13)+5=−212(-13) + 5 = -21.

Worth noting

Writing 3(a−1)3(a - 1) as 3a−13a - 1 gives −4-4; a sign slip in the last step gives 6.

Concept
Substituting an expression for the variable and solving for a parameter
Typical time
120 s
Your time
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The rule this testsLinear equations in one variable
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