Solve the following linear equation.

Question

6(x−11)=196\left(x-11\right)=196(x−11)=19

x=x=x=

(Note: if the answer is an infinite repeating decimal your answer must be in fraction form. So 0.333... = 130.333...\ =\ \frac{1}{3}0.333... =
3
1
​
)

Answer 1

To solve the given linear equation, we need to simplify and isolate \( x \).

Starting from the equation:

\[ 6(x - 11) = 196 \]

First, we distribute the 6 on the left side:

\[ 6x - 66 = 196 \]

Next, we'll isolate \( 6x \) by adding 66 to both sides of the equation:

\[ 6x = 196 + 66 \]

Calculating the right side:

\[ 196 + 66 = 262 \]

So now we have:

\[ 6x = 262 \]

Now, we divide by 6 to solve for \( x \):

\[ x = \frac{262}{6} \]

To simplify \(\frac{262}{6}\), we can divide both the numerator and the denominator by their greatest common divisor. The GCD of 262 and 6 is 2.

So we simplify:

\[ x = \frac{262 \div 2}{6 \div 2} = \frac{131}{3} \]

Thus, the solution to the equation is:

\[ x = \frac{131}{3} \]

Answer 2

Solve the following linear equation.

−y2+3=2\frac{-y}{2}+3=2
2
−y
​
+3=2

y=y=y=

Answer 3

To solve the equation

\[ -\frac{y}{2} + 3 = 2, \]

we'll start by isolating the term with \( y \).

First, subtract 3 from both sides:

\[ -\frac{y}{2} = 2 - 3. \]

Calculating the right side gives:

\[ -\frac{y}{2} = -1. \]

Next, to eliminate the negative sign, we multiply both sides by -1:

\[ \frac{y}{2} = 1. \]

Now, we multiply both sides by 2 to solve for \( y \):

\[ y = 2 \cdot 1 = 2. \]

Thus, the solution is:

\[ y = 2. \]