Question #5513

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.

Expert's answer

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.

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.

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