Answer :
Let's solve the equation step-by-step and verify the solution.
We have the equation:
[tex]\[
\frac{2}{3} x + 7 = 5
\][/tex]
and we're checking if [tex]\( x = -6 \)[/tex] is a solution.
Step 1: Substitute [tex]\( x = -6 \)[/tex] into the equation.
First, we'll replace [tex]\( x \)[/tex] with [tex]\(-6\)[/tex] in the equation:
[tex]\[
\frac{2}{3}(-6) + 7
\][/tex]
Step 2: Calculate [tex]\(\frac{2}{3}(-6)\)[/tex].
Multiply [tex]\(\frac{2}{3}\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
\frac{2}{3} \times (-6) = \frac{-12}{3} = -4
\][/tex]
Step 3: Add 7 to the result from Step 2.
Now add 7:
[tex]\[
-4 + 7 = 3
\][/tex]
The left side of the equation evaluates to 3.
Step 4: Compare the left side and right side.
The right side of the original equation is 5. So we compare:
[tex]\[
3 \neq 5
\][/tex]
Since the left side (3) does not equal the right side (5), [tex]\( x = -6 \)[/tex] is not a solution to the equation.
We have the equation:
[tex]\[
\frac{2}{3} x + 7 = 5
\][/tex]
and we're checking if [tex]\( x = -6 \)[/tex] is a solution.
Step 1: Substitute [tex]\( x = -6 \)[/tex] into the equation.
First, we'll replace [tex]\( x \)[/tex] with [tex]\(-6\)[/tex] in the equation:
[tex]\[
\frac{2}{3}(-6) + 7
\][/tex]
Step 2: Calculate [tex]\(\frac{2}{3}(-6)\)[/tex].
Multiply [tex]\(\frac{2}{3}\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
\frac{2}{3} \times (-6) = \frac{-12}{3} = -4
\][/tex]
Step 3: Add 7 to the result from Step 2.
Now add 7:
[tex]\[
-4 + 7 = 3
\][/tex]
The left side of the equation evaluates to 3.
Step 4: Compare the left side and right side.
The right side of the original equation is 5. So we compare:
[tex]\[
3 \neq 5
\][/tex]
Since the left side (3) does not equal the right side (5), [tex]\( x = -6 \)[/tex] is not a solution to the equation.
