Skill: Interpret solutions to linear equations

A solution to a linear equation is a value of the variable that makes the left side and right side equal. To interpret a solution, explain what the value means in the situation and check it in the original equation.

Example: A taxi charges a 5$starting fee plus$$3$per mile. The total cost is$$20$. How many miles were traveled?

Let $m$ represent the number of miles. The equation is

$$3m+5=20$$

Step 1: Solve the equation

Subtract $5$ from both sides:

$$3m=15$$

Divide both sides by $3$:

$$m=5$$

Step 2: Interpret the solution

The solution $(m=5)$ means the taxi traveled 5 miles.

Step 3: Verify the solution

Substitute $5$ into the original equation:

$$3(5)+5=20$$ $$15+5=20$$ $$20=20$$

Both sides are equal, so $(m=5)$ is the solution. It also makes sense in the situation because a distance of $5$ miles is valid.