Question

look at the diagram.
which equation can be used to solve for x?
$13x - 14 = 90$ $13x - 14 = 180$ $5x - 14 = 90$ $5x - 14 = 180$
solve for x.
$x = \square$

Explanation:

Part 1: Find the equation to solve for \( x \)

Step1: Identify the right angle

The angle at \( F \) between \( EF \) and \( FD \) is a right angle (\( 90^\circ \)), so the sum of \( (9x - 14)^\circ \) and \( (4x)^\circ \) should equal \( 90^\circ \).

Step2: Set up the equation

Add the two angles: \( (9x - 14) + 4x = 90 \). Combine like terms: \( 13x - 14 = 90 \).

Step1: Add 14 to both sides

Starting with \( 13x - 14 = 90 \), add 14 to each side: \( 13x - 14 + 14 = 90 + 14 \), which simplifies to \( 13x = 104 \).

Step2: Divide by 13

Divide both sides by 13: \( \frac{13x}{13} = \frac{104}{13} \), so \( x = 8 \).

Answer:

\( 13x - 14 = 90 \)

Part 2: Solve for \( x \)