Question

What number should be added to both sides of the equation x - 7/8 = - 5 to find the value of x?

Answer 1

To find the value of x, we need to isolate the variable.

The given equation is x - 7/8 = -5.

To isolate x, we need to get rid of the constant term on the same side as x.

To do that, we add the opposite of the constant term to both sides of the equation.

The opposite of -5 is +5, so we add 5 to both sides of the equation:

x - 7/8 + 5 = -5 + 5.

Simplifying the expression, we get:

x - 7/8 + 5 = 0.

Combining the terms on the left side, we have:

x - 7/8 + 5 = 0.

Now, the common denominator of the terms on the left side is 8. So, we need to rewrite the whole expression with the common denominator:

x - 7/8 + 5 = 0.

x + (-7/8) + 5 = 0.

Adding the fractions with the same denominator, we get:

x + (-7/8) + 5 = 0.

x + (-7/8) + (40/8) = 0.

Combining the terms on the left side, we have:

x + (-7/8) + (40/8) = 0.

(x + 40 - 7)/8 = 0.

(x + 33)/8 = 0.

To solve for x, we multiply both sides of the equation by 8:

8 * (x + 33)/8 = 0 * 8.

Simplifying the expression, we get:

x + 33 = 0.

To solve for x, we subtract 33 from both sides of the equation:

x + 33 - 33 = 0 - 33.

x = -33.

Therefore, the value of x is -33.