Question

for each value of x, determine whether it is a solution to -1 = \\(\frac{x}{9}\\) - 5.

is it a solution?	yes	no
72	\\(\circ\\)	\\(\circ\\)
27	\\(\circ\\)	\\(\circ\\)
-90	\\(\circ\\)	\\(\circ\\)
-45	\\(\circ\\)	\\(\circ\\)

Explanation:

The equation given is \(-1=\frac{x}{9}-5\). We need to check for each value of \(x\) (72, 27, -90, -45) whether it satisfies the equation.

Step 1: Solve the equation for \(x\) (optional, but helps to know the solution)

Start with \(-1=\frac{x}{9}-5\).
Add 5 to both sides: \(-1 + 5=\frac{x}{9}-5 + 5\)
Simplify: \(4=\frac{x}{9}\)
Multiply both sides by 9: \(x = 4\times9=36\). Wait, but maybe we can just substitute each value. Wait, maybe I misread the equation. Wait, the equation is \(-1=\frac{x}{9}-5\)? Let's re - check. Or maybe it's \(-1=\frac{x}{9}-5\)? Let's solve it again.

\(-1=\frac{x}{9}-5\)

Add 5 to both sides: \(-1 + 5=\frac{x}{9}\)

\(4=\frac{x}{9}\)

Multiply both sides by 9: \(x = 36\). But the given \(x\) values are 72, 27, -90, -45. Wait, maybe the equation is \(-1=\frac{x}{9}-5\) is wrong? Wait, maybe the equation is \(-1=\frac{x}{9}-5\) or maybe \(-1=\frac{x}{9}-5\)? Wait, let's check each value by substitution.

For \(x = 72\):

Substitute \(x = 72\) into \(\frac{x}{9}-5\): \(\frac{72}{9}-5=8 - 5 = 3\). Is \(3=-1\)? No. So \(x = 72\) is not a solution.

For \(x = 27\):

Substitute \(x = 27\) into \(\frac{x}{9}-5\): \(\frac{27}{9}-5 = 3-5=-2\). Is \(-2=-1\)? No. So \(x = 27\) is not a solution.

For \(x=-90\):

Substitute \(x = - 90\) into \(\frac{x}{9}-5\): \(\frac{-90}{9}-5=-10 - 5=-15\). Is \(-15=-1\)? No. So \(x=-90\) is not a solution.

For \(x = - 45\):

Substitute \(x=-45\) into \(\frac{x}{9}-5\): \(\frac{-45}{9}-5=-5 - 5=-10\). Is \(-10=-1\)? No. Wait, this is confusing. Wait, maybe the equation is written incorrectly? Wait, maybe the equation is \(-1=\frac{x}{9}-5\) or maybe \(-1=\frac{x}{9}-5\)? Wait, maybe I made a mistake in the equation. Wait, looking at the image, the equation is \(-1=\frac{x}{9}-5\)? Wait, no, maybe it's \(-1=\frac{x}{9}-5\) or maybe the equation is \(-1=\frac{x}{9}-5\). Wait, let's re - examine the image. The equation is \(-1=\frac{x}{9}-5\)? Wait, the user's image shows " - 1 = x/9 - 5". So we have to check each x:

Wait, maybe I miscalculated. Let's re - do the substitution:

1. For \(x = 72\):

\(\frac{72}{9}-5=8 - 5 = 3\). \(3
eq - 1\) → No.

1. For \(x = 27\):

\(\frac{27}{9}-5 = 3-5=-2\). \(-2
eq - 1\) → No.

1. For \(x=-90\):

\(\frac{-90}{9}-5=-10 - 5=-15\). \(-15
eq - 1\) → No.

1. For \(x=-45\):

\(\frac{-45}{9}-5=-5 - 5=-10\). \(-10
eq - 1\) → No.

Wait, this is strange. Maybe the equation is \(-1=\frac{x}{9}-5\) is wrong? Or maybe the equation is \( - 1=\frac{x}{9}-5\) with a different sign? Wait, maybe the equation is \( - 1=\frac{x}{9}-5\) or maybe \( - 1=\frac{x}{9}-5\). Alternatively, maybe the equation is \( - 1=\frac{x}{9}-5\) and we made a mistake. Wait, let's solve the equation again:

\(-1=\frac{x}{9}-5\)

Add 5 to both sides: \(4=\frac{x}{9}\)

Multiply by 9: \(x = 36\). So none of the given \(x\) values (72, 27, -90, -45) are solutions? But that seems odd. Wait, maybe the equation is written as \(-1=\frac{x}{9}-5\) or maybe it's \(-1=\frac{x}{9}-5\) with a typo. Alternatively, maybe the equation is \(-1=\frac{x}{9}-5\) and the \(x\) values are different. Wait, the \(x\) values in the table are 72, 27, -90, -45. So according to the substitution:

• \(x = 72\): No
• \(x = 27\): No
• \(x=-90\): No
• \(x=-45\): No

Answer:

• For \(x = 72\): No
• For \(x = 27\): No
• For \(x=-90\): No
• For \(x=-45\): No