Question

part b
solve each equation. then choose the correct unit (dollars, ounces, or hours) that the variable represents. express any fractions in the form a/b.

$3x + 6 = 27$
$x = \boxed{}$; (dollars, ounces, hours) $\boxed{}$

$6x + 3 = 27$
$x = \boxed{}$; (dollars, ounces, hours) $\boxed{}$

$27x + 3 = 6$
$x = \boxed{}$; (dollars, ounces, hours) $\boxed{}$

Explanation:

For the equation \( 3x + 6 = 27 \)

Step 1: Subtract 6 from both sides

To isolate the term with \( x \), we subtract 6 from both sides of the equation.
\( 3x + 6 - 6 = 27 - 6 \)
Simplifying, we get \( 3x = 21 \).

Step 2: Divide both sides by 3

To solve for \( x \), we divide both sides of the equation by 3.
\( \frac{3x}{3} = \frac{21}{3} \)
Simplifying, we get \( x = 7 \).

Since the value 7 is a reasonable measure for ounces (e.g., quantity of a substance), dollars (e.g., cost per unit), or hours (e.g., time), but typically, such linear equations for ounces (quantity), dollars (cost), or hours (time) can all apply, but let's assume a context. However, the unit here can be any of the three, but let's pick ounces (or dollars or hours, but let's proceed).

Step 1: Subtract 3 from both sides

To isolate the term with \( x \), we subtract 3 from both sides of the equation.
\( 6x + 3 - 3 = 27 - 3 \)
Simplifying, we get \( 6x = 24 \).

Step 2: Divide both sides by 6

To solve for \( x \), we divide both sides of the equation by 6.
\( \frac{6x}{6} = \frac{24}{6} \)
Simplifying, we get \( x = 4 \).

The unit here can be any of the three, but let's pick hours (or dollars or ounces, depending on context).

Step 1: Subtract 3 from both sides

To isolate the term with \( x \), we subtract 3 from both sides of the equation.
\( 27x + 3 - 3 = 6 - 3 \)
Simplifying, we get \( 27x = 3 \).

Step 2: Divide both sides by 27

To solve for \( x \), we divide both sides of the equation by 27.
\( \frac{27x}{27} = \frac{3}{27} \)
Simplifying, we get \( x = \frac{1}{9} \).

The unit here can be any of the three, but let's pick dollars (or ounces or hours, depending on context).

Answer:

\( x = 7 \); (dollars, ounces, hours) ounces (or dollars or hours, depending on context)

For the equation \( 6x + 3 = 27 \)