Question

1. solve for x. 19x - 28 6x + 7 x =

Explanation:

Step1: Use the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length. So, \(2(6x + 7)=19x - 28\).

Step2: Expand the left - hand side

Expand \(2(6x + 7)\) to get \(12x+14\). The equation becomes \(12x + 14=19x - 28\).

Step3: Move the \(x\) terms to one side and constants to the other

Subtract \(12x\) from both sides: \(14=19x-12x - 28\), which simplifies to \(14 = 7x-28\). Then add \(28\) to both sides: \(14 + 28=7x\), so \(42 = 7x\).

Step4: Solve for \(x\)

Divide both sides by \(7\): \(x=\frac{42}{7}\).

Answer:

\(x = 6\)