Solve the following equation for xx. Express your answer in the simplest form.

Question

minus, 6, left parenthesis, minus, 8, x, plus, 7, right parenthesis, equals, 7, left parenthesis, 5, x, plus, 6, right parenthesis
−6(−8x+7)=
7(5x+6)

Answer 1

To solve the equation

$$-6(-8x+7)=7(5x+6),$$

let's start by simplifying both sides.

Step 1: Distribute on the left side.

$$-6(-8x)+(-6)(7)=48x-42$$

So, the left side becomes:

$$48x-42.$$

Step 2: Distribute on the right side.

$$7(5x)+7(6)=35x+42.$$

So, the right side becomes:

$$35x+42.$$

Step 3: Rewrite the equation with the simplified expressions.

We now have:

$$48x-42=35x+42.$$

Step 4: Move all terms involving $x$ to one side and constant terms to the other side.

Subtract $35x$ from both sides:

$$48x-35x-42=42.$$

This simplifies to:

$$13x-42=42.$$

Next, add $42$ to both sides:

$$13x=42+42.$$

This simplifies to:

$$13x=84.$$

Step 5: Solve for $x$.

Divide both sides by $13$:

$$x=\frac{84}{13}.$$

Thus, the solution in its simplest form is:

$$\boxed{{\displaystyle \frac{84}{13}}}.$$