### Solving Linear Equations Practice Question #### Question 2

Solve the following linear equation:  A. x = -3
B. x = 2
C. x = -2
D. x = 3

### Step by Step Solution

• #### Step 1

It is easier to find x if we remove the denominator, 3, from the equation. To do so, we can multiply both sides of the equation by 3. • #### Step 2

Now, both 3 cancel off each other. We successfully removed the denominator. • #### Step 3

The equation becomes: Notice that, to continue further, we need to remove the brackets in the Right hand Side (RHS). • #### Step 4

Now, 2 multiply by x gives 3x. • #### Step 5

Next, 3 multiply by +2 gives +6. • #### Step 6

The equation becomes: • #### Step 7

Notice that we can remove 3x by adding -3x to both sides of the equation. Now the equation becomes:

2x -3x +4 = 3x -3x +6

On the RHS, 3x and -3x cancel off. We now have: • #### Step 8

We can add 2x with -3x. This gives -x • #### Step 9

Also, notice that we can remove +4 on the LHS by adding -4 to both sides of the equation. Now the equation becomes:

2x -3x +4 -4 = 6 -4

+4 and -4 cancel off. We now have: • #### Step 10

Now, on the RHS, minus 6 with 4 gives 2.

The equation becomes -x = 2. • #### Step 11

Now, we can get x by multiplying both sides by -1. The equation becomes: • #### Step 12

Now, -1 multiplying by -x gives x.
Similarly, -1 multiplying by 2 gives -2.

Therefore we get x = -2. The answer is C. 