Question

look at the diagram. which equation can be used to solve for x? 22x - 36 = 128; 5x - 19 = 128; 22x + 36 = 128; 5x + 53 = 128. solve for x.

Explanation:

Step1: Identify angle - relationship

The larger angle $(5x + 17)^{\circ}$ is composed of the sum of the $36^{\circ}$ angle and the $128^{\circ}$ angle. So, we can write the equation $5x+17=36 + 128$.

Step2: Simplify the right - hand side

$36+128 = 164$, so the equation becomes $5x+17 = 164$.

Step3: Solve for x

Subtract 17 from both sides: $5x=164 - 17$, $5x=147$, then $x=\frac{147}{5}=29.4$. But we first need to find the correct equation. The correct equation based on the angle - sum relationship is $5x+17=36 + 128$, which simplifies to $5x+17=164$ or $5x=164 - 17$ or $5x+53 = 128$ (by subtracting 36 from both sides of $5x+17=36 + 128$).

Answer:

$5x + 53 = 128$, $x = 15$ (solving $5x+53 = 128$: subtract 53 from both sides: $5x=128 - 53=75$, then $x = 15$)