Algebra - Mixed Practice (Up to Linear Equations)

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Algebra - Mixed Practice (Up to Linear Equations)

This set of worksheets builds on the previous two sets. We still see some pre-algebra problems, as well as some problems involving converting phrases to algebraic expressions, and simplifying those expressions. Introduced in this set are problems involving setting up and solving basic one-variable equations.

Worksheet 3.1

In this worksheet we ask students to write expressions and equations, but do not ask them to solve.

multiplying and dividing fractions
percentages
writing algebraic expressions
writing equations

Worksheet 3.2

In this worksheet we ask students to solve equations, including ones they've written themselves. There are no equations with variables on both sides of the equation, but there are some where combining of like terms and distributive property come into play.

simplifying fractions
adding and subtracting fractions
solving equations
writing and solving equations

Worksheet 3.3

Equations in this worksheet require students to move variables from one side of the equation to the other, as well as using distributive property, and combining like terms. In addition, we ask specific questions, such as "How much will five pens cost?", and in most cases, the question asked will not be the variable solved for, so this worksheet gives students practice in returning to the problem to find out what they're being asked.

order of operations with positives and negatives
solving equations
writing and solving equations

Worksheet Sets in this Series

Worksheets for this section are below the index. Click the "Overview" link to get a more detailed view of the entire series.

Lesson by Mr. Twitchell

Handouts/Worksheets

Mixed Practice 3.1

12
3
·
4
9
=
3
11
·
22
5
=
4 ·
3
5
=
2 ÷
3
2
=
5
6
÷
2
3
=
10% of 355 =
240, increased by 5% =
10% of 10 more than a number =
Ten more than a number, discounted by 40% =

Write each of the following as equations
Ten more than a number is 15.
Four less than a number is 80.
Two more than three times a number is 50.
Three more than half a number is ten less than that number.
The result of adding two numbers is 40.
A number, plus six more than that number is three times the number.
Half of a number, plus two thirds of a number, is 14.
Walter's age, plus Walter's age in 10 years is 44.
The cost of 12 bags of chips is $13.80. (Hint: unknown is the cost of one bag)
Lida got back $1.25 in change after spending $28.20. (Hint: unknown is the amount she started with)
Albert is twice as tall as he was five years ago, when he was 12" shorter than he is now.

Mixed Practice 3.1: Answer Key

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Mixed Practice 3.2

Simplify each expression completely

18
40
=
32
120
=
3
9
+
2
3
=
4
5
-
1
10
=
5 -
11
3
+
2
4
=
3
7
(
1
2
+
2
3
) =

Solve each equation below.
3x + 2 = 11
2(x - 4) = 20
3x + 2x + 1 = 21
5(x + 2) + 3(x - 5) = 51
3x +
1
2
x = 35
0.9x - 0.5 = 10.3
1.5x + 0.2x = 34
A number, plus twice that number is 45.
Half of a number, plus one third of a number, is 25.
Sixteen more than five times a number is 41.
Two thirds of a number is equal to 12.
The sum of twice a number and 1.2 is 7.6.
Twice the sum of a number and 1.2 is 7.6.
Half of the sum of a number and two more than that number is 37.

Mixed Practice 3.2: Answer Key

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Mixed Practice 3.3

5 - 3[-4 - (-10)]+ 20 =
12 - (-2)[5 - (-1)] =
-4 + (-3)[8 - 2(1 + 3)] =
4 +
2
3
(1 +
3
2
) =
2 + 3{5 - 2[3 - 4(1 + 1)]} =
2x + 3x + 20 = x
3(x + 2) = 4(x - 1) + 4
2
5
(x + 5) = 10
1
2
x +
2
5
x = 18
3x + 12 = 2x - 12
x = 3(x - 10)
2(x + 1) + 3(x + 2) = 6(x - 5)
Twice a number, plus 32 is four times the number. Find half of the number.
Three times five less than a number is equal to twice the number. What is the sum of the number and 10?
The sum of Joe's age and Joe's age in ten years is equal to three times Joe's age. How old will Joe be next year?
The cost of 12 apples is $4.20 more than the cost of 8 apples. What is the cost of 6 apples?
An item is discounted 12%. The resulting price is $4.50 less than the original price. What would the price be if it had been discounted 30%?
The price of an item is inflated by 20%, and then by an additional $10. The result is the same as doubling the original price. What would the price have been if it had been discounted by 50%?
Joan counts her legos, and finds that the number of legos she owns is 2000 less than three times the number of legos she owns. If she gave away 30% of her legos, how many would she have left?
The amount of money I have is $5.00 more than it was when I had half as much as I have now. If I double my money, how much will I have?

Mixed Practice 3.3: Answer Key

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