Solving Linear Equations

Steps to Solve a Linear Equation for a Variable

Let's solve the equation \(2x - 5 = 7\):

3. Isolate the Variable on One Side: \(2x = 7 + 5\)
4. Combine Like Terms: \(2x = 12\)
7. Continue Isolating the Variable: Divide both sides by 2: \(x = 6\)
8. Check Your Solution: Substitute \(x = 6\) back into the original equation: \(2(6) - 5 = 7\)
9. Write Down the Solution: \(x = 6\) is the solution.

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Writing Algebraic form of a pattern rule

Steps to Find Algebraic Form of Linear Pattern Rule

1. Identify the Pattern:
   • Examine the given sequence or pattern.
   • Note the relationship between the position of each term and its value.
2. Determine the Common Difference or Ratio:
   • For linear patterns, determine the common difference between consecutive terms.
   • If the pattern is increasing, note how much each term increases by.
   • If the pattern is decreasing, note how much each term decreases by.

The Unyielding Pillars of Success

A Deep Dive into the Importance of Focus and Hard Work

Success, that elusive pinnacle of achievement, is not a mystical summit reserved for a chosen few but a tangible reality that unfolds through the interplay of two steadfast allies: focus and hard work. These virtues, often celebrated as the cornerstones of personal and professional triumph, lay the groundwork for individuals to forge their destinies and carve a meaningful legacy.

Focus, akin to a laser beam honing in on its target, directs our efforts with precision towards a singular objective. In a world brimming with diversions and constant stimuli, the ability to maintain unwavering attention on a goal distinguishes the triumphant from the mediocre. Whether navigating the academic labyrinth, scaling the peaks of a career, or pursuing personal aspirations, the capacity to stay focused becomes a navigational compass, ensuring that energy and resources are channeled efficiently.

System of Linear Equations-1

System of linear equations (Grade 10 Math) Word Problems

1. Sara is 5 years older than Jane. The sum of their ages is 35. How old is each?


2. Sarah has $20 in nickels and dimes. She has a total of 160 coins. How many of each does she have?


3. A person invests $4,000 in two accounts, one yielding 4% interest and the other 6% interest. The total annual interest is $220. How much is in each account?


4. A chemical solution contains 20% salt. How many liters of a 30% solution must be added to 5 liters of a 10% solution to make a 25% solution?


5. Alex is driving from City A to City B, which is 240 miles away. He drives the first 120 miles at 60 mph and the rest at 40 mph. How long does the trip take?

Making Graphs- bar graphs, histograms and line graphs

Part A: Bar Graphs

1. Create a bar graph to represent the number of books read by students in a class. Use the following data:

   Student	Books Read
   Alice	5
   Bob	7
   Cindy	4
   David	6
   Emily	8

1s and 10s

Identifying 1s and 10s

Objective: To help Grade 1 students recognize and differentiate between 1s and 10s.

1.

5

Is this a group of 1s or 10s? Write your answer in the circle.

2.

10

Is this a group of 1s or 10s? Write your answer in the circle.

Order of Operations Worksheet

Instructions: Solve each expression using the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division - left to right, Addition and Subtraction - left to right). Simplify fractions and mixed numbers where necessary. Show your work.

1. Calculate: \(2 + 3 \cdot (4 - 1)^2 \div 5 = ?\)

2. Simplify: \(\frac{5}{8} + \frac{3}{4} \cdot \frac{1}{2} = ?\)

3. Evaluate: \(3^2 \cdot 2 - 4 + \frac{1}{2} \div 2 = ?\)