Final answer:
When two parallel lines are intersected by a transversal, alternate interior angles are congruent. To find the value of x in the expression (9x + 7)((10 - x)), we set each factor equal to 0 and solve for x. The value of x is -7/9.
Step-by-step explanation:
Given m || n, we know that the lines m and n are parallel. When two parallel lines are intersected by a transversal, alternate interior angles are congruent. The given expression (9x + 7)((10 - x)) represents the product of two binomials. To find the value of x, we can set the expression equal to 0 and solve for x.
To solve the equation (9x + 7)((10 - x)) = 0, we set each factor equal to 0 and solve for x. We get 9x + 7 = 0 or 10 - x = 0.
Solving these equations, we find x = -7/9 or x = 10.
Since x cannot be equal to 10 (as it would make the denominator of the expression undefined), the value of x is -7/9.