Solve (2x - 1)/3 - (x - 2)/4 = (x + 5)/6.

Linear and Quadratic Equations · Question 11 of 66

Question 11

HardOriginal question

Solve $\frac{2x - 1}{3} - \frac{x - 2}{4} = \frac{x + 5}{6}$ .

\frac{3}{4}

Correct answerYour answer

\frac{8}{3}

Correct answerYour answer

\frac{20}{3}

Correct answerYour answer8Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Multiply every term by 12: $4(2x - 1) - 3(x - 2) = 2(x + 5)$ .
Expand: $8x - 4 - 3x + 6 = 2x + 10$ .
Simplify: $5x + 2 = 2x + 10$ , so $3x = 8$ .
Hence $x = \frac{8}{3}$ .

Worth noting

The trap is $-3(x - 2)$ : it is $-3x + 6$ , not $-3x - 6$ (which leads to $\frac{20}{3}$ ). Multiplying the right side by 1 instead of 2 gives $\frac{3}{4}$ .

Concept: Clearing fractions when a minus sign stands before a fraction
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsLinear equations in one variable

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Solve 2x−13−x−24=x+56\frac{2x - 1}{3} - \frac{x - 2}{4} = \frac{x + 5}{6}32x−1​−4x−2​=6x+5​.

Explanation

Solve $\frac{2x - 1}{3} - \frac{x - 2}{4} = \frac{x + 5}{6}$ .