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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
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to 5x−15. You can think of this as (5x−15) is being multiplied by
5
1
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.
5
1
​
(5x − 15) = 9x + 9
= 9x + 9

1 answer

To solve the equation \( \frac{5}{1}(5x - 15) = 9x + 9 \), we will first simplify the left side using the distributive property.

  1. Distribute \( \frac{5}{1} \) (which is just 5) to each term inside the parentheses: \[ 5(5x - 15) = 5 \cdot 5x - 5 \cdot 15 = 25x - 75 \]

So, our equation now looks like this: \[ 25x - 75 = 9x + 9 \]

  1. Next, we want to get all the terms involving \( x \) on one side and the constant terms on the other side. We can subtract \( 9x \) from both sides: \[ 25x - 9x - 75 = 9 \] Simplifying that: \[ 16x - 75 = 9 \]

  2. Now, we add 75 to both sides to isolate the term with \( x \): \[ 16x = 9 + 75 \] Simplifying this gives: \[ 16x = 84 \]

  3. Finally, we solve for \( x \) by dividing both sides by 16: \[ x = \frac{84}{16} \] Simplifying further gives: \[ x = \frac{21}{4} \quad \text{or} \quad x = 5.25 \]

Thus, the solution to the equation is: \[ x = \frac{21}{4} \text{ or } x = 5.25 \]