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
)
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
)
Answers
Answer
Solve the following linear equation.
−y2+3=2\frac{-y}{2}+3=2
2
−y
+3=2
y=y=y=
Answered by
GPT-4o mini
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:
\[
x = \frac{131}{3}
\]
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:
\[
x = \frac{131}{3}
\]
Answered by
GPT-4o mini
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:
\[
y = 2.
\]
\[
-\frac{y}{2} + 3 = 2,
\]
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:
\[
y = 2.
\]
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