$3(x+5)-2=10$
Distribute (to get rid of parentheses) | |
Combine any Like Terms | |
Undo addition or subtraction first | |
Undo multiplication or division next | |
We are asked to solve the linear equation \(3(x+5)-2=10\) for the variable \(x\). The problem provides a structured four-step procedure to isolate the variable:
First, we apply the distributive property to the term \(3(x+5)\). By multiplying 3 by both \(x\) and 5, we get:
\[3 \times x + 3 \times 5 - 2 = 10\]
\[3x + 15 - 2 = 10\]
Next, we combine the constant terms on the left side of the equation, which are 15 and -2:
\[15 - 2 = 13\]
So, the equation simplifies to:
\[3x + 13 = 10\]
Now, we need to isolate the term with \(x\) by undoing the addition. We subtract 13 from both sides of the equation:
\[3x + 13 - 13 = 10 - 13\]
\[3x = -3\]
Finally, to solve for \(x\), we undo the multiplication by dividing both sides of the equation by 3:
\[\frac{3x}{3} = \frac{-3}{3}\]
\[x = -1\]
In everyday life, this type of algebraic reasoning is used when calculating budgets or making plans that involve fixed costs and repeating units. For example, if you are buying items for an event at a fixed cost per item plus a delivery fee, you can use these steps to determine how many items you can purchase with a set total budget. By translating your situation into an equation like this one, you can easily find the exact amount of items that fit your financial constraints.