Chapter 4.4, Problem 51STP

To determine

To find: the equation which is not graphed on the number line

Answer to Problem 51STP

The correct answer is option (J).

Explanation of Solution

Given:

Calculation:

Consider the following graph showing that a solution on number line:

The objective is to find which solution of the equation is NOT graphed on the number line above.

In the above figure, the dot at $-2$ on the number line shows that the solution is $x=-2$ .

In option (F), the equation is as follows:

  $12=-6x$

Solve the above equation as follows:

  $12=-6x$ Write the original equation

  $\frac{12}{-6}=\frac{-6x}{-6}$ Divide both sides by $-6$

  $-2=x.$ Simplify

Therefore, the solution of the equation $12=-6x$ is $x=-2$ .

So, the solution of the equation $12=-6x$ in option (F) is graphed on the number line above. Hence, eliminate the statement of option (F).

In option (G), the equation is as follows:

  $8x=-16.$

Solve the above equation as follows:

  $8x=-16$ Write the original equation

  $\frac{8x}{8}=\frac{-16}{8}$ Divide both sides by 8

  $x=-2.$ Simplify

Therefore, the solution of the equation $8x=-16$ is $x=-2$ .

So, the solution of the equation $8x=-16$ in option (G) is graphed on the number line above. Hence, eliminate the statement of option (G).

In option (H), the equation is as follows:

  $-14=7x.$

Solve the above equation as follows:

  $-14=7x$ Write the original equation

  $\frac{-14}{7}=\frac{7x}{7}$ Divide both sides by 7

  $-2\text{ =}x$ . Simplify

Therefore, the solution of the equation $-14=7x$ is $x=-2$ .

So, the solution of the equation $-14=7x$ in option (H) is graphed on the number line above Hence, eliminate the statement of option (H).

In option (J), the equation is as follows:

  $-18x=-36$ .

Solve the above equation as follows:

  $-18x=-36$ Write the original equation

  $\frac{-18x}{-18}=\frac{-36}{-18}$ Divide both sides by -18.

  $x=2.$ Simplify

Therefore, the solution of the equation $-18x=-36$ is $x=2.$

So, the solution of the equation -18x = -36 in option (J) is NOT graphed on the number line above.

Conclusion:

Therefore, the correct answer is option (J).