Question

Solve the following linear equation.



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

Solve the following linear equation.





−y2+3=2\frac{-y}{2}+3=2
2
−y
​
+3=2



y=y=y=

Answer 2

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 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:

\[
y = 2.
\]