Questions: Look at the diagram. Which equation can be used to solve for x ? 7x+28=67 7x+18=67 30x+5=67 30x-5=67 Solve for x. x=

Look at the diagram. Which equation can be used to solve for x ? 7x+28=67 7x+18=67 30x+5=67 30x-5=67 Solve for x. x=
Transcript text: Look at the diagram. Which equation can be used to solve for $x$ ? $7 x+28=67$ $7 x+18=67$ $30 x+5=67$ $30 x-5=67$ Solve for $x$. \[ x=\square \]
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Solution

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Solution Steps

Step 1: Identify the relationship between the angles

The diagram shows three angles that form a straight line at point A. The sum of angles on a straight line is 180 degrees.

Step 2: Set up the equation

The given angles are 23°, 67°, and (7x - 5)°. Therefore, the equation is: \[ 23 + 67 + (7x - 5) = 180 \]

Step 3: Simplify the equation

Combine like terms: \[ 23 + 67 - 5 + 7x = 180 \] \[ 85 + 7x = 180 \]

Step 4: Solve for x

Subtract 85 from both sides: \[ 7x = 95 \] Divide by 7: \[ x = \frac{95}{7} \] \[ x = 13.57 \]

Final Answer

\[ x = 13.57 \]

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