Mathematics
Grade 7
15 min
Solve linear equations word problems
Solve linear equations word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify the unknown quantity in a word problem and assign a variable to it.
Translate verbal phrases into algebraic expressions.
Formulate one-step and two-step linear equations from word problem scenarios.
Solve linear equations using inverse operations.
Interpret the numerical solution in the context of the original word problem.
Check the reasonableness of their solutions.
Ever wonder how math helps solve everyday puzzles like figuring out how much change you'll get or sharing items fairly? 💰 Let's discover how to turn tricky word problems into simple equations!
In this lesson, you'll learn a powerful strategy to break down word problems, translate them into linear equations, and solve for the unknown. This skill is essential for appl...
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Key Concepts & Vocabulary
TermDefinitionExample
VariableA symbol, usually a letter (like x, y, or n), that represents an unknown number or quantity in an equation.In the problem 'A number increased by 5 is 12', we can let 'x' be the unknown number.
ConstantA fixed value that does not change in an expression or equation.In the equation $x + 7 = 15$, the numbers 7 and 15 are constants.
Algebraic ExpressionA combination of variables, constants, and mathematical operations (addition, subtraction, multiplication, division) that does not contain an equality sign.$2x + 3$ or $y - 8$
Linear EquationAn equation where the highest power of the variable is 1. It states that two algebraic expressions are equal.$3x - 4 = 11$ or $y + 5 = 20$
KeywordsSpecific words or phrases in a word problem that indicate wh...
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Core Formulas
Properties of Equality
If $a = b$, then:
1. $a + c = b + c$ (Addition Property)
2. $a - c = b - c$ (Subtraction Property)
3. $ac = bc$ (Multiplication Property)
4. $a/c = b/c$ (Division Property, where $c \neq 0$)
These properties allow you to perform the same operation on both sides of an equation. This keeps the equation balanced and helps you isolate the variable to find its value.
General Form of a Linear Equation
$ax + b = c$
Many word problems can be translated into this form, where 'x' is the variable, 'a' is its coefficient, and 'b' and 'c' are constants. This structure guides you in setting up and solving equations.
5 more steps in this tutorial
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Challenging
A company packages 4 of its products into a gift box that weighs 0.5 kg. The total weight of the filled box is 3.7 kg. Which equation can be used to find the weight, 'w', of one product?
A.4(w + 0.5) = 3.7
B.0.5w + 4 = 3.7
C.4w + 0.5 = 3.7
D.w + 4 + 0.5 = 3.7
Challenging
Kara and Simon are reading the same 320-page book. Kara reads 20 pages per day. Simon started 3 days earlier and reads 15 pages per day. After how many days, 'd', since Kara started reading will they be on the same page?
A.9 days
B.5 days
C.12 days
D.They will never be on the same page.
Challenging
A rectangular garden has a length that is 5 feet less than twice its width. The garden is surrounded by 50 feet of fencing. The owner also bought a 10-foot gate which is part of the perimeter. What is the width of the garden?
A.15 feet
B.25 feet
C.20 feet
D.10 feet
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