Question

Solving an Equation with Rational Numbers
Jerome solved the equation 1
3
x + 5
6
= 1 as shown.

1. Subtraction property
of equality: 1
3
x + 5
6
− 5
6
= 1
1
− 5
6
2. LCD: 1
3
x = 1
6
− 5
6
3. Multiply by the
reciprocal: ( 3
1
) 1
3
x = −4
6
( 3
1
)
4. Solve and simplify: x = −12
6
= −2
Analyze Jerome’s steps. In which step did he make an error?
In step 1, he needed to add StartFraction 5 Over 6 EndFraction to both sides of the equation.
In step 2, the LCD was not used correctly to make equivalent fractions.
In step 3, the correct reciprocal was not multiplied to both sides.
In step 4, the answer was not reduced correctly.

Answer 1

He made an error in step 2.

Reason: after subtracting 5/6 from both sides you get
(1/3)x = 1 − 5/6 = 6/6 − 5/6 = 1/6.
Jerome wrote 1/6 − 5/6 (or otherwise misused the LCD), which gave (1/3)x = −4/6 and led to the wrong final answer. The correct solution is

(1/3)x = 1/6 → x = 3·(1/6) = 1/2.