*I mean, I've ridden trains between Chicago and New York, but I've never plotted when my train will pass another. To multiply with a percent, we convert it to a decimal. If you want to try the new plan and spend only each month, how many texts can you send? *In this lesson, we'll not only practice solving problems that can be translated into linear equations, we'll also focus on problems you may encounter in your life - problems not involving trains passing each other. If we solve for x by subtracting 35 from both sides, we get x = 37. They can be a bit more complex, like this: 15 less than four times a number is 57.

*I mean, I've ridden trains between Chicago and New York, but I've never plotted when my train will pass another. To multiply with a percent, we convert it to a decimal. If you want to try the new plan and spend only each month, how many texts can you send? *In this lesson, we'll not only practice solving problems that can be translated into linear equations, we'll also focus on problems you may encounter in your life - problems not involving trains passing each other. If we solve for x by subtracting 35 from both sides, we get x = 37. They can be a bit more complex, like this: 15 less than four times a number is 57.

The second train is going 85 mph for t time, or 85t. In other words, when do the two distances add up to the total distance, 800 miles. Now, we divide both sides by 160, and we get t = 5.

The first train is traveling at a rate of 75 mph, so the distance it covers in t time is 75t.

Solving an equation numerically means that only numbers represented explicitly as numerals (not as an expression involving variables), are admitted as solutions.

Solving an equation symbolically means that expressions that may contain known variables or possibly also variables not in the original equation are admitted as solutions. Note that the distinction between known variables and unknown variables is made in the statement of the problem, rather than the equation.

A solution of an equation is often also called a root of the equation, particularly but not only for algebraic or numerical equations.

A problem of solving an equation may be numeric or symbolic.

Ok, before we go, why don't we try that train problem, you know, just to show that we can. Another train leaves New York at the same time, traveling on a parallel track to Chicago at 85 mph. We're trying to find how much time it will take, or t.

traveling to New York, which is 800 miles away, at 75 mph.

However, in some areas of mathematics the convention is to reserve some variables as known and others as unknown.

When writing polynomials, the coefficients are usually taken to be known and the indeterminates to be unknown, but depending on the problem, all variables may assume either role.

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