Question

look at the diagram. which equation can be used to solve for x? 17x + 37 = 90, 17x - 37 = 90, 12x + 42 = 90, 12x + 32 = 90. solve for x.

Explanation:

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

Step 1: Identify the angle relationship

The diagram shows a right angle at \( C \), so the sum of the angles \( 37^\circ \) and \( (12x + 5)^\circ \) should be \( 90^\circ \) (since they are complementary angles in a right angle).

Step 2: Set up the equation

We add the two angles and set them equal to \( 90^\circ \):
\( 37 + (12x + 5) = 90 \)
Simplify the left - hand side: Combine like terms \( 37+5 = 42 \), so the equation becomes \( 12x + 42=90 \)

Part 2: Solve for \( x \)

Step 1: Subtract 42 from both sides

We start with the equation \( 12x + 42 = 90 \). Subtract 42 from both sides to isolate the term with \( x \):
\( 12x+42 - 42=90 - 42 \)
\( 12x=48 \)

Step 2: Divide both sides by 12

Now, divide both sides of the equation \( 12x = 48 \) by 12 to solve for \( x \):
\( x=\frac{48}{12} \)
\( x = 4 \)

Answer:

(Equation):
The equation to solve for \( x \) is \( 12x + 42 = 90 \)