Solve the equation below. What's the value of h?

Question

There are many ways you could solve this equation. We need to get h alone on one side, and a constant number alone on the other side. Since h is inside the parentheses on the left, we can use the distributive property to rewrite the equation without parentheses. Go for it. Distribute the
5
1
​
to 5h−15. You can think of this as (5h−15) is being multiplied by
5
1
​
.
5
1
​
(5h − 15) = 9h + 9
= 9h + 9
You got it!
You rewrote the left side of the equation without parentheses. Now, we can keep solving by making sure there are only h terms on one side of the equation. Let’s get rid of the h terms on the left so there are only h terms on the right side. What move can you make next to get rid of h on the left, while keeping the equation balanced?
5
1
​
(5h−15)
=
9h+9

h − 3
=
9h + 9

Add h to both sides

Divide both sides by h

Multiply both sides by h

Subtract h from both sides
You got it!
You can subtract h from both sides of the equation to get rid of the h on the left, so that all the h terms are on the right side of the equation. Record subtracting h from both sides now.
5
1
​
(5h−15)
=
9h+9

h − 3
=
9h + 9
−

h
−

h
Good work!
Subtract h from both sides of the equation to get rid of the h on the left, so that all the h terms are on the right side of the equation.
5
1
​
(5h−15)
=
9h+9

h − 3
=
9h + 9
−
h
−
h

=
Excellent!
Now that you have all the variables on the right, you can start thinking about how to make sure all the constant numbers are only on one side. What move can you make to get rid of the 9 on the right, so that 8h is alone on the right side, while keeping the equation balanced?
5
1
​
(5h−15)
=
9h+9

h − 3
=
9h + 9
−
h
−
h

−3
=
8h + 9

Divide both sides by 9

Add 9 to both sides of the equation

Subtract 9 from both sides of the equation
Excellent!
We can subtract 9 from both sides to get rid of 9, so that 8h is alone on the right side of the equation. Record subtracting 9 from each side.
5
1
​
(5h−15)
=
9h+9

h − 3
=
9h + 9
−
h
−
h

−3
=
8h +9
−

9
−

9
Nice!
Subtract 9 from each side of the equation to get rid of 9 on the right, so that 8h is alone on the right side of the equation.
5
1
​
(5h−15)
=
9h+9

h − 3
=
9h + 9
−
h
−
h

−3
=
8h +9
−
9
−
9

=

Answer 1

Let's go through the equation step-by-step based on the process you've outlined.

Starting from the beginning with the equation:

\[ 5(5h - 15) = 9h + 9 \]

First, using the distributive property:

\[ 5 \cdot 5h - 5 \cdot 15 = 9h + 9 \]

This simplifies to:

\[ 25h - 75 = 9h + 9 \]

Now, subtract \(9h\) from both sides to get:

\[ 25h - 9h - 75 = 9 \]

This simplifies to:

\[ 16h - 75 = 9 \]

Next, add \(75\) to both sides:

\[ 16h = 9 + 75 \]

which simplifies to:

\[ 16h = 84 \]

Now, divide both sides by \(16\):

\[ h = \frac{84}{16} \]

Reducing this fraction:

\[ h = \frac{21}{4} \]

So, the value of \(h\) is:

\[ h = 5.25 \]

Thus, the final answer is that \(h = \frac{21}{4}\) or \(h = 5.25\).