Question

Owen solves the equation below and his steps are shown. When he plugged his solution back into the original equation, he did not get a true statement. Please help him identify THE FIRST STEP in which he made an error.

ORIGINAL EQUATION: 3 (x-4) = -4 - 2 (x-5)

STEP 1: 3x - 12 = -4 - 2x +10
STEP 2: 3x -12 = -2x - 4 +10
STEP 3: 3x - 12 = -2x + 6
STEP 4: subtract -2x from either side
STEP 5: x - 12 = 6
STEP 6: add 12 to either side
STEP 7: x=18

Answer 1

THE FIRST STEP in which he made an error is step 4, instead of subtracting 2x from either side of the equation, he is to add 2x to either side of the equation.

The correct value of x is 3.6

Explanation:

To solve the given equation, we will follow the steps below;

3 (x-4) = -4 - 2 (x-5)

step 1 : open the parentheses

That is, 3x - 12 = -4 - 2x + 10

Step 2 : simplify, that is, yo can add the or subtract like terms

hence

3x - 12 = -2x -4 + 10

step 3 :

3x - 12 = -2x + 6

step 4 : Add 2x to both-side of the equations in order to nullify the 2x on the right-hand side of the equation

3x + 2x - 12 = -2x + 2x + 6

step 5:

5x - 12 = 6

step 6: Add 12 to both-side of the equation

5x - 12 + 12 = 6 + 12

step 7

5x = 18

Step 8: divide both-side of the equation by 5

5x/5 = 18/5

step 9:

x =3.6

THE FIRST STEP in which he made an error is step 4, instead of subtracting 2x from either side of the equation, he is to add 2x to either side of the equation.

That is why he got the wrong answer.