6x - 7 = 0 and 12x + 4c = 82 are two equations in x. If they have the same solution, then c = ?

Steps to Solve

1. Solve the First Equation for x

Start with the equation (6x - 7 = 0).

Add 7 to both sides to isolate the term with (x):

$$6x = 7$$

Next, divide both sides by 6:

$$x = \frac{7}{6}$$

2. Set up the Second Equation

Now, look at the second equation (12x + 4c = 82).

We will substitute the value of (x) we found earlier into this equation.

3. Substitute x into the Second Equation

Substituting (x = \frac{7}{6}) into the second equation:

$$12\left(\frac{7}{6}\right) + 4c = 82$$

Which simplifies to:

$$14 + 4c = 82$$

4. Isolate c

Subtract 14 from both sides:

$$4c = 82 - 14$$

This gives us:

$$4c = 68$$

5. Solve for c

Now, divide both sides by 4:

$$c = \frac{68}{4}$$

This simplifies to:

$$c = 17$$