Questions: x ÷ 3 = 2x = 5x = x / 4 = 4x = 4(x / 3) = 24 / y = y ÷ 2 = 6y =

Transcript text: \[ x \div 3= \] \[ 2 x= \] \[ 5 x= \] \[ \frac{x}{4}= \] \[ 4 x= \] \[ 4\left(\frac{x}{3}\right)= \] \[ \frac{24}{y}= \] \[ y \div 2= \] \[ 6 y=\text {. } \]

Solution

Solution Steps

To solve the given equations, we need to find the value of \( x \) and \( y \) and then use these values to solve the subsequent equations.

For \( x \div 3 = 7 \), solve for \( x \).
For \( \frac{24}{y} = 8 \), solve for \( y \).
Use the values of \( x \) and \( y \) to solve the remaining equations.

Step 1: Solve for \( x \)

Given the equation \( x \div 3 = 7 \), we can multiply both sides by 3 to isolate \( x \): \[ x = 7 \times 3 = 21 \]

Step 2: Solve for \( y \)

From the equation \( \frac{24}{y} = 8 \), we can rearrange it to find \( y \) by multiplying both sides by \( y \) and then dividing by 8: \[ y = \frac{24}{8} = 3.0 \]

Step 3: Calculate Additional Expressions

Using the values of \( x \) and \( y \), we can compute the following:

\( 2x = 2 \times 21 = 42 \)
\( 5x = 5 \times 21 = 105 \)
\( \frac{x}{4} = \frac{21}{4} = 5.25 \)
\( 4x = 4 \times 21 = 84 \)
\( 4\left(\frac{x}{3}\right) = 4\left(\frac{21}{3}\right) = 4 \times 7 = 28.0 \)
\( y \div 2 = \frac{3.0}{2} = 1.5 \)
\( 6y = 6 \times 3.0 = 18.0 \)

Final Answer

The results are: \[ x = 21, \quad 2x = 42, \quad 5x = 105, \quad \frac{x}{4} = 5.25, \quad 4x = 84, \quad 4\left(\frac{x}{3}\right) = 28.0, \quad y = 3.0, \quad y \div 2 = 1.5, \quad 6y = 18.0 \] Thus, the boxed final answers are: \[ \boxed{x = 21}, \quad \boxed{2x = 42}, \quad \boxed{5x = 105} \]

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