Questions: Question Completion Status: QUESTION 1 Determine the number by which both sides of the equation must be multiplied or divided, as specified, to obtain just x on the left side. 2/7 x=6 ; multiply by 6 -2/7 7/2 7 QUESTION 2 Solve and check the equation.

Solution Steps

For Question 1, to isolate \( x \) on the left side of the equation \(\frac{2}{7} x = 6\), we need to multiply both sides by the reciprocal of \(\frac{2}{7}\), which is \(\frac{7}{2}\).

For Question 2, solve the equation by isolating the variable on one side and then check the solution by substituting it back into the original equation.

Given the equation

\[ \frac{2}{7} x = 6 \]

we multiply both sides by the reciprocal of \(\frac{2}{7}\), which is \(\frac{7}{2}\):

\[ x = 6 \cdot \frac{7}{2} = 21 \]

Consider the equation

\[ 3x + 4 = 10 \]

To isolate \( x \), we first subtract 4 from both sides:

\[ 3x = 10 - 4 \]

This simplifies to:

\[ 3x = 6 \]

Next, we divide both sides by 3:

\[ x = \frac{6}{3} = 2 \]

To verify our solution, we substitute \( x = 2 \) back into the original equation:

\[ 3(2) + 4 = 6 + 4 = 10 \]

Since both sides are equal, the solution is confirmed.

Final Answer