Solve for r:
$7r + 21 = 49r$
$7r + 21 = 49r$
Solve for r:
$7r + 21 = 49r$
The given equation is a linear equation in the variable \(r\), which is:
\[7r + 21 = 49r\]
To solve for \(r\), we need to isolate the variable on one side of the equation. We notice that there are terms involving \(r\) on both sides, so our first objective is to group these terms together.
To group the terms containing \(r\), we subtract \(7r\) from both sides of the equation. This operation preserves the equality:
\[7r + 21 - 7r = 49r - 7r\]
Simplifying both sides, we obtain:
\[21 = 42r\]
Now, the variable \(r\) is isolated on one side with a coefficient of 42.
To isolate \(r\) completely, we divide both sides of the equation by 42:
\[\frac{21}{42} = \frac{42r}{42}\]
Simplifying the fraction on the left side, we have:
\[r = \frac{21}{42} = \frac{1}{2} = 0.5\]
Thus, the value of \(r\) that satisfies the original equation is \(0.5\).
Imagine you are setting up a small business where you sell custom stickers. The cost of materials to start is \$@@MATH_TOKEN_22@@, and the production cost per sticker is \$\(7\). If you decide to sell your stickers for \$\(49\) each, you can use an algebraic equation to find out the number of stickers you need to sell to reach a point where your total costs match a certain projection. Solving for \(r\) helps you determine the exact quantity needed to balance your financial model, ensuring your business stays on track.