Unit 3: Handout 7 Writing Equations

• Write an equation from a verbal sentence.

• Translate an equation into a verbal sentence

• Determine if an equation is true by substituting values into the equation.

• An expression is a mathematical phrase.

• We can translate a verbal phrase into a mathematical expression.

• Example "a number increased by 4" can be translated into the expression n + 4

• An equation is a mathematical sentence.

• An equation has an equals sign, and expression does not

• Word problems containing words or phrases that describe equality, such as is, equals, is equal to, and is the same as can be translated into equations.

• "A number increased by 4 is 10" can be written as the equation:

• n + 4 = 10

• is means =

• "A number decreased by 8" tells us that a number we don't know should be subtracted by 8

• x - 8 =

• The words after the word is, tells us what should be on the right side of the equation. So 12 should be on the right side of the equation.

• x - 8 = 12

2x + 0​ = 24

2x = 24

2 2​

x = 12

Rewrite the problem

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Combine the variable terms on the left side by doing the inverse operation of -4x. Add 4x to both sides.

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​​Combine "like terms" on each side.

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Now combine the constants on the right side by doing the inverse operation of -13. Add 13 to both sides.

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Combine "like terms" on each side.

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Isolate the variable by dividing each side by the coefficient 2.

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​Simplify each side and get your final answer.

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​If you can solve equations with ease you may skip the next video!