Solving Linear Equations Practice Question

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Question 2

Solve the following linear equation:

Algebra equation (2x+4)/3 = x +2

Answer

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Select and check your answer...

A. x = -3
B. x = 2
C. x = -2
D. x = 3

Step by Step Solution

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    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.

    Multiply both sides by 3
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    Step 2

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

    Both 3 cancel of each other
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    Step 3

    The equation becomes:

    Algebra equation 2x +4 = 3(x +2)

    Notice that, to continue further, we need to remove the brackets in the Right hand Side (RHS).

    Remove brackets in 3(x +2)
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    Step 4

    Now, 2 multiply by x gives 3x.

    2 multiply by x gives 3x
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    Step 5

    Next, 3 multiply by +2 gives +6.

    3 multiply by +2 gives +6.
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    Step 6

    The equation becomes:

    Algebra equation 2x +4 = 3x +6
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    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:

    Algebra equation 2x -3x +4 = +6
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    Step 8

    We can add 2x with -3x. This gives -x

    Algebra equation -x +4 +6
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    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:

    Algebra equation -x = +6 -4
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    Step 10

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

    The equation becomes -x = 2.

    Algebra equations -x = 2
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    Step 11

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

    Multiply both sides with -1
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    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.

    Answer is x = -2