Answer to Question #5513 in Algebra for Lavora Moses

Question

What is the difference between an equation and an expression? Include an example of each. Can you solve for a variable in an expression? Explain. Can you solve for a variable in an equation? Explain. Write a mathematical phrase or sentence for your classmates to translate.

Answer 1

What is the difference between an equation and an expression? Include an example of each.

The difference between an equation and an expression can be compared to the difference between a phrase and a sentence in grammar.

An expression (i.e. 4x, 10 + 2, etc.) could be compared to a subject or an object. By themselves, they mean very little. When you add a verb (=), you get a complete sentence (i.e. 4x = 10 + 2).

Can you solve for a variable in an expression? Explain.

No, not in a expression. x represents the variable in the expression 4x. There are an infinite number of possibilities you can substitute for the x, so it cannot be solved.

Can you solve for a variable in an equation? Explain.

Yes. Because we have a complete sentence we can make sense of the equation 4x = 10 + 2. Because we know that 10 + 2 can be written as 12 and mean the same thing, we can substitue the correct number for the x so the expressions on both sides of the = sign represent the same value. 4 * 3 = 10 + 2.

Write a mathematical phrase or sentence for your classmates to translate.

You have been assigned to ship 4800 gizmos to a job site. How many boxes would have to be loaded on each truck if you could pack 8 pieces in each box and you had 3 trucks available.