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

There are many ways you could solve this equation. We need to get x alone on one side, and a constant number alone on the other side. Since x 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 5x−15. You can think of this as (5x−15) is being multiplied by
5
1
​
.
5
1
​
(5x − 15) = 9x + 9
= 9x + 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 x terms on one side of the equation. Let’s get rid of the x terms on the left so there are only x terms on the right side. What move can you make next to get rid of x on the left, while keeping the equation balanced?
5
1
​
(5x−15)
=
9x+9

x − 3
=
9x + 9

Divide both sides by x

Multiply both sides by x

Subtract x from both sides

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

x − 3
=
9x + 9
−

x
−

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

x − 3
=
9x + 9
−
x
−
x

=

1 answer

Let’s solve the equation step by step as described.

  1. You start with the expression on the left side, \( \frac{5}{1} (5x - 15) = 9x + 9 \).
  2. Distributing \( \frac{5}{1} \) to \( (5x - 15) \), we have:
    \( 5(5x) - 5(15) = 25x - 75 \).

So, the equation becomes: \[ 25x - 75 = 9x + 9. \]

  1. Next, to isolate \( x \), we want all the \( x \) terms on one side. You mentioned subtracting \( x \) from both sides: \[ 25x - 75 - 9x = 9. \]

  2. This simplifies to: \[ (25x - 9x) - 75 = 9, \] \[ 16x - 75 = 9. \]

  3. Now, we can get rid of the constant on the left side (add 75 to both sides): \[ 16x - 75 + 75 = 9 + 75, \] \[ 16x = 84. \]

  4. Now, to solve for \( x \), divide both sides by 16: \[ x = \frac{84}{16}. \]

  5. Simplifying this fraction gives: \[ x = \frac{21}{4}. \]

Therefore, the value of \( x \) is \( \frac{21}{4} \) or \( 5.25 \) in decimal form.