Question

look at the diagram. which equation can be used to solve for x? 5x + 30 = 90; 5x + 60 = 90; 5x + 60 = 180; 5x + 30 = 180. solve for x.

Explanation:

Step1: Isolate the term with x

Subtract 30 from both sides of the equation \(5x + 30=90\).

$$5x+30 - 30=90 - 30$$

$$5x=60$$

Step2: Solve for x

Divide both sides of the equation \(5x = 60\) by 5.

$$\frac{5x}{5}=\frac{60}{5}$$

$$x = 12$$

To find the correct equation from the options:
Since the sum of angles around a point is \(360^{\circ}\), and we have a right - angle (\(90^{\circ}\)) and a \(60^{\circ}\) angle, and two angles \(x^{\circ}\) and \((4x)^{\circ}\).
The sum of these angles \(x + 4x+60 + 90=360\) is wrong. But if we consider a linear - pair or some angle - relationship within a part of the figure.
If we assume that the angles \(x\) and \(4x\) and a \(60^{\circ}\) angle and a right - angle are related in such a way that they form a straight - line (sum of angles on a straight - line is \(180^{\circ}\)).
The equation \(x+4x + 60+90 - 180=0\), which simplifies to \(5x+60 = 90\).
The correct equation to solve for \(x\) from the given options is \(5x + 30=90\).

Answer:

The value of \(x\) is \(12\) and the correct equation to solve for \(x\) is \(5x + 30=90\).