ACT Math Elementary Algebra Linear Equations Solving and Setting Up from Word Problems

Elementary Algebra — Linear Equations: Solving and Setting Up from Word Problems

What This Is and Why It Matters for the ACT

Elementary algebra, specifically solving and setting up linear equations from word problems, appears in the Math section of the ACT. It's a fundamental concept, appearing on almost every Math test, with moderate difficulty.

Key Concepts (What You Must Know)

• Linear equation: An equation in which the highest power of the variable (x) is 1.
• Variable: A letter representing a value that can change.
• Coefficient: A number multiplied by a variable.
• Constant: A number that doesn't change.
• Solving an equation: Finding the value of the variable that makes the equation true.

Step-by-Step Strategy for This Topic

1. Read the word problem carefully and identify the key information.
2. Translate the word problem into a linear equation using variables and coefficients.
3. Use inverse operations to isolate the variable (addition, subtraction, multiplication, or division).
4. Check your work by plugging the solution back into the original equation.
5. Manage your time: allocate 1-2 minutes per question.

⚠️ Don't forget to check your units when solving equations with variables in different units.

How It’s Tested on the ACT

The Math section will present multiple-choice questions with five answer choices. You'll be given a word problem and asked to translate it into a linear equation and solve for the variable. Be careful of distractors like: * Incorrectly translating the word problem into an equation * Forgetting to check units or signs * Not using inverse operations correctly

Common Mistakes & Exam Traps

1. The mistake: Forgetting to check units or signs.
   • Why it happens: Rushing through the problem or misreading the units.
   • How to avoid it: Double-check your units and signs before solving the equation.
   • Exam board insight: The ACT penalizes incorrect units or signs.
2. The mistake: Not using inverse operations correctly.
   • Why it happens: Misunderstanding the concept of inverse operations.
   • How to avoid it: Review the concept of inverse operations and practice using them.
   • Exam board insight: The ACT expects students to use inverse operations correctly.
3. The mistake: Incorrectly translating the word problem into an equation.
   • Why it happens: Misreading the word problem or misunderstanding the concept of variables.
   • How to avoid it: Read the word problem carefully and review the concept of variables.
   • Exam board insight: The ACT penalizes incorrect translations.

Practice Questions (3-5 questions)

Question 1: Tom has been saving money for a new bike and has $120 in his piggy bank. He wants to buy a bike that costs $180. If he saves $5 per week, how many weeks will it take him to have enough money to buy the bike?

Options: A) 10 weeks, B) 12 weeks, C) 15 weeks, D) 18 weeks, E) 20 weeks

Answer: C) 15 weeks

Explanation: Let x be the number of weeks it takes Tom to save enough money. The equation is 120 + 5x = 180. Solving for x, we get x = 12. However, this is the number of weeks after Tom already has $120. To find the number of weeks it takes him to save the remaining amount, we subtract 12 from the total number of weeks: 12 - 12 = 0 weeks (he already has the money) + 3 weeks (he needs to save 5*3 = 15 dollars) = 3 weeks. However, this is a trick question, and the correct answer is actually 12 weeks because we need to add 12 to the 3 weeks he already has.