Question

Write an equation with the variable on each side of the equals sign, at least one fractional coefficient, and a solution of -6. Discuss the steps you used.

Short answer

The required equation is $\frac{1}{2}x=-9-x$.

Step-by-step solution

Step 1. State the concept.

An equation is solved by carrying out the same operations on both sides such that the variable is isolated on one side and its value is on the other side.

Step 2. List the objective.

The objective is to write an equation with the variable on each side of the equals sign, at least one fractional coefficient, and a solution of -6.

Step 3. Formulate the equation.

Let the variable be $x$.

Start with the solution:$x=-6$

Multiply a fraction, say $\frac{3}{2}$to both sides to get a fractional coefficient:$x\times \frac{3}{2}=-6\times \frac{3}{2}$

Simplify:$\frac{3}{2}x=-9$

Divide the variable part into two parts:$x+\frac{1}{2}x=-9$

Move any of the variable term to the right-hand side:$\frac{1}{2}x=-9-x$

So, the required equation is $\frac{1}{2}x=-9-x$.