Unit 3: Handout 7 Writing Equations

Review + Check of Translating Equations

Follow along with the lesson and answer the questions along the way! This is intended to help you review Handout 7 because it has been a few days since we've learned this lesson!

I can

• 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.

Key Ideas

• 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

Key Ideas

• 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

Open Ended

Write this as an expression: $6 dollars less than the cost of an xbox.

A number decreased by 8 is 12

• 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

Open Ended

Write an equation to represent the situation:

A number decreased by 8 is 12

Multiple Choice

Three less than twice a number

• 2x-3

• 3x-2

• 3-2x

• 2-3x

Match

Match the following:

• Division

• Addition

• Multiplication

• Subtraction

Quotient

Sum

Product

Difference

• Quotient

• Sum

• Product

• Difference

Multiple Choice

Translate: 10 less that half a number is equivalent to 8.  

• 10 - 1⁄2x = 8 

• 1⁄2x + 10 = 8

• 1⁄2x - 10 = 8

• 10x - 0.5 = 8

Multiple Choice

Translate into a verbal expression. $$7x+6=10$$  

• Seven times a number decreased by six is ten.

• The quantity of six times a number plus seven is ten.

• Six more than seven times a number is ten.

• Seven more than six times a number is ten.

Multiple Choice

Translate: Five less than the product of seven and a number is the same as thirteen.

• 7s - 5 = 13

• 5 - 7 + s = 13

• 13 = 7(s - 5) 

• 5 - 7s = 13

Multiple Choice

In order to solve an equation, we must get variables on one side of an equation, and constants on the opposite side.

• False

• True

​See below for another solving option!

​6x - 13 = 11 - 4x

6x + 4x - 13 = 11 - 4x + 4x

2x - 13 = 11 + 0

2x - 13 + 13 = 11 + 13

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're still stuck try this next method! It's a little unconventional but it might help you!

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

Multiple Choice

Identify the steps to solve for b

• Add 6 to both sides then divide both sides by 5

• Add 6 to both sides then multiply both sides by 5

• Subtract 6 from both sides then multiply both sides by 5

• Subtract 6 from both sides then divide both sides by 5

Multiple Choice

$$5x-1=19$$  

• $$x=4$$  

• $$x=10$$  

• $$x=5$$  

• $$x=15$$  

Multiple Choice

What is the first step you should take to solve this problem?

1 + 4n - 6n = 1 - 8n

• subtract 8n to both sides

• multiply 6n to both sides

• combine the like terms 4n + -6n

Multiple Choice

$$24\ =\ 3\left(3x\ -7\right)$$

• $$x\ =\ -9$$  

• $$x\ =\ 5$$  

• $$x\ =3$$  

• $$x\ =\ 7$$  

Multiple Choice

$$r\ +\ 11\ +\ 8r\ =\ 29$$  

• $$r\ =0$$  

• $$r\ =\ 1$$  

• $$r\ =\ 2$$  

• $$r\ =\ 3$$  

Fill in the Blank

$$5x\ +\ 18\ =\ 12x\ +\ 4$$  

Multiple Choice

$$-5\left(4x\ -\ 2\right)\ =\ -2\left(3\ +6x\right)$$  

• $$x\ =\ 2$$  

• $$x\ =\ 8$$  

• $$x\ =\ -2$$  

• $$x\ =\ -8$$