What does 5x mean? What does[ggfrac] x/5[/ggfrac] mean?

5x means 5 times x. [ggfrac]x/5[/ggfrac] means x divided by 5.

How can you find the value of x in the expression x + 4 = 5?

I want to get x alone to find out what it is. To get x alone on the left side, subtract 4. Since I always do the same thing to both sides of the equation, I also have to subtract 4 on the right. Then x = 1.

How can you find the value of x in the expression 5x = 20?

5x means 5 times x. I can imagine that there are 5 bags containing cookies and there are 20 cookies in all. Then x represents how many cookies are in each bag. I want to have just one x on the left, which means I have to divide by 5 on both sides. Then x = 4.

What are inverse operations?

Addition and subtraction are inverse operations, and multiplication and division are inverse operations. In 2x = 6, the operation between 2 and x is multiplication, so I have to use division to solve for x.

How can you expand the expression 3(x – 5)?

The 3 on the outside of the parentheses means that everything on the inside gets multiplied by 3. 3 times x is 3x and 3 times 5 is 15. Then the expanded form is 3x – 15.

What are the operations in the equation 4x – 5 = 7? What operations do you need to use to solve for x?

The operations are multiplication and subtraction. So to solve for x, I need to use the inverse operations: division and addition.

To solve 4x – 5 = 7, should you divide first or add first?

I could do either first, but if I divide first, I have to divide 5 by 4 and 7 by 4, which means that I have to work with fractions. That would take longer but still get the right answer. However, if I add 5 to both sides first, then the rest of the solution is much easier.

How can you solve x3-2=2?

[ggfrac]x/3[/ggfrac] means x divided by 3, so the inverse operation is multiplication. I also need to add to isolate the variable. It is simpler to first add 2 on both sides, and then to multiply both sides by 3, but working in the opposite order would also result in the same answer. Then x= 12.

What are two different ways you can solve 2(x – 3) = 8?

Method 1: Distribute 2 across the expression in the parentheses, so that I have 2x – 6 = 8, and then solve by adding 6 to both sides, and then dividing both sides by 2. Method 2: First divide both sides by the factor 2, so that I have x – 3 = 4. Then solve by adding 3 to both sides. Method 2 is more efficient.

To solve 2x + 3 = 5, Sylvia first subtracted 5 from both sides. What did she do wrong?

Because Sylvia did the same operation to both sides, the equation is still correct: the two sides still equal. However, she is no closer to finding out the value of x. She should instead subtract 3 on both sides, which gets her closer to having x alone on the left side.

Solve Algebraic Equations (2-Step)

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WHAT ARE 2-STEP ALGEBRAIC EQUATIONS?

Students learn to find all factor pairs for a whole number in the range 1-100. Students will also recognize that a whole number is a multiple of each of its factors. They will determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number and whether a given whole number in the range 1-100 is prime or composite.

To better understand 2-step algebraic equations…

WHAT ARE 2-STEP ALGEBRAIC EQUATIONS?. Students learn to find all factor pairs for a whole number in the range 1-100. Students will also recognize that a whole number is a multiple of each of its factors. They will determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number and whether a given whole number in the range 1-100 is prime or composite. To better understand 2-step algebraic equations…

LET’S BREAK IT DOWN!

Solve equations with addition and multiplication.

To rake leaves for your neighbors, you charge $4 for every hour you work, plus a flat fee of $3 for showing up. If you raked one lawn for $23, how many hours did you work? We can represent this using an equation, if we let x be the number of hours worked. We write 4x + 3 = 23. To get x on its own, we need to get rid of everything else on the left side. We can do that by using inverse operations. The inverse of + 3 is – 3, so we subtract 3 on both sides. Then we have 4x = 20. Next, 4x means 4 times x, and the inverse is to divide by 4. So we divide both sides by 4, and then we have x = 5. You worked for 5 hours! Now you try: Find x if 3x + 5 = 17.

Solve equations with addition and multiplication. To rake leaves for your neighbors, you charge $4 for every hour you work, plus a flat fee of $3 for showing up. If you raked one lawn for $23, how many hours did you work? We can represent this using an equation, if we let x be the number of hours worked. We write 4x + 3 = 23. To get x on its own, we need to get rid of everything else on the left side. We can do that by using inverse operations. The inverse of + 3 is – 3, so we subtract 3 on both sides. Then we have 4x = 20. Next, 4x means 4 times x, and the inverse is to divide by 4. So we divide both sides by 4, and then we have x = 5. You worked for 5 hours! Now you try: Find x if 3x + 5 = 17.

How can we check our work?

We solved 4x + 3 = 23, and found that x = 5. If we want to check our answer, we can do that by substituting the answer into the original equation. Now that we know that x = 5, we can substitute 5 for x in the equation, so that we get 4(5) + 3 = 23. 4 times 5 is 20, and adding 3 to that is 23. Since both sides of the equal sign have the same value, we know that our work checks out! Now you try: Check if x = 2 is true for 6x + 4 = 16.

How can we check our work? We solved 4x + 3 = 23, and found that x = 5. If we want to check our answer, we can do that by substituting the answer into the original equation. Now that we know that x = 5, we can substitute 5 for x in the equation, so that we get 4(5) + 3 = 23. 4 times 5 is 20, and adding 3 to that is 23. Since both sides of the equal sign have the same value, we know that our work checks out! Now you try: Check if x = 2 is true for 6x + 4 = 16.

Solve equations with multiplication and subtraction.

You got a deal at the local record store. You bought 5 records and got $7 off. If your total came to $98, how much was each record, assuming they all cost the same amount? If we let x be the price of a record, our equation becomes 5x – 7 = 98. First we want to get rid of – 7, and the inverse operation to subtraction is addition. So, we add 7 on both sides. Now we have 5x = 105. If we want to have only one x on the left side, we can divide both sides by 5. We get x = 21. So, each record cost $21! Now you try. Find x if 3x – 7 = 29.

Solve equations with multiplication and subtraction. You got a deal at the local record store. You bought 5 records and got $7 off. If your total came to $98, how much was each record, assuming they all cost the same amount? If we let x be the price of a record, our equation becomes 5x – 7 = 98. First we want to get rid of – 7, and the inverse operation to subtraction is addition. So, we add 7 on both sides. Now we have 5x = 105. If we want to have only one x on the left side, we can divide both sides by 5. We get x = 21. So, each record cost $21! Now you try. Find x if 3x – 7 = 29.

Solve two-step equations with fractions.

$Solve two-step equations with fractions.$

You took out one third of the money in your piggy bank, and you already have $8 in your pocket. If the total amount of money you have now is $16, how much was in the piggy bank? If we let x be the amount of money in the piggy bank, then our equation is [ggfrac]x/3[/ggfrac]+8=16. Remember that the line between x and 3 means division. To solve for x, first we subtract 8 from both sides, and now we have [ggfrac]x/3[/ggfrac]=8. Since x is divided by 3, the inverse operation is multiplication, so we multiply both sides by 3 to get x alone. Now we have x=24. That means that originally you had $24 in the piggy bank! Now you try: Find x if [ggfrac]x/5[/ggfrac]+2=22.

Solve two-step equations with fractions. You took out one third of the money in your piggy bank, and you already have $8 in your pocket. If the total amount of money you have now is $16, how much was in the piggy bank? If we let x be the amount of money in the piggy bank, then our equation is [ggfrac]x/3[/ggfrac]+8=16. Remember that the line between x and 3 means division. To solve for x, first we subtract 8 from both sides, and now we have [ggfrac]x/3[/ggfrac]=8. Since x is divided by 3, the inverse operation is multiplication, so we multiply both sides by 3 to get x alone. Now we have x=24. That means that originally you had $24 in the piggy bank! Now you try: Find x if [ggfrac]x/5[/ggfrac]+2=22.

Solve Algebraic Equations (2-Step)

Discussion Questions

Vocabulary

Reading Material

LET’S BREAK IT DOWN!

Solve equations with addition and multiplication.

How can we check our work?

Solve equations with multiplication and subtraction.

Solve two-step equations with fractions.

Practice Word Problems

Practice Number Problems

Teacher Resources

Lesson Plan

Teacher Guide

Answer Key

Assessment

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