Question

for each value of y, determine whether it is a solution to 9 - 2y = 29.

y	is it a solution?
6	yes ○ no ○
-10	yes ○ no ○
-7	yes ○ no ○

Explanation:

We are given the equation \(9 - 2y = 29\) and we need to check for each value of \(y\) (9, 6, -10, -7) if it is a solution. A solution to an equation is a value that when substituted into the equation makes the left - hand side equal to the right - hand side.

Step 1: Solve the equation \(9 - 2y=29\) for \(y\)

Subtract 9 from both sides of the equation:
\(9 - 2y-9=29 - 9\)
\(-2y = 20\)
Divide both sides by - 2:
\(y=\frac{20}{-2}=- 10\)

Step 2: Check \(y = 9\)

Substitute \(y = 9\) into the left - hand side of the equation \(9-2y\):
\(9-2\times9=9 - 18=-9\)
Since \(-9
eq29\), \(y = 9\) is not a solution.

Step 3: Check \(y = 6\)

Substitute \(y = 6\) into the left - hand side of the equation \(9-2y\):
\(9-2\times6=9 - 12=-3\)
Since \(-3
eq29\), \(y = 6\) is not a solution.

Step 4: Check \(y=-10\)

Substitute \(y = - 10\) into the left - hand side of the equation \(9-2y\):
\(9-2\times(-10)=9 + 20=29\)
Since \(29 = 29\), \(y=-10\) is a solution.

Step 5: Check \(y=-7\)

Substitute \(y=-7\) into the left - hand side of the equation \(9-2y\):
\(9-2\times(-7)=9 + 14=23\)
Since \(23
eq29\), \(y=-7\) is not a solution.

Answer:

• For \(y = 9\): No
• For \(y = 6\): No
• For \(y=-10\): Yes
• For \(y=-7\): No