Q1. Solve for :

Background

Topic: Solving Linear Equations

This question tests your ability to solve a simple linear equation for the variable .

Key Terms and Formulas

• Linear equation: An equation involving only the first power of the variable.

• Isolate the variable: Move all terms involving to one side and constants to the other.

Step-by-Step Guidance

1. Identify the equation:

2. Subtract $11x$:

3. Simplify both sides:

   (expression to be calculated)

Try solving on your own before revealing the answer!

Q2. Solve for :

Background

Topic: Solving Linear Equations with Fractions

This question tests your ability to solve a linear equation where the variable is multiplied by a fraction.

Key Terms and Formulas

• Fractional coefficient: The variable is multiplied by .

• To isolate , multiply both sides by the reciprocal of , which is $7$.

Step-by-Step Guidance

1. Identify the equation:

2. Multiply both sides by $7x$:

3. Simplify both sides:

   (expression to be calculated)

Try solving on your own before revealing the answer!

Q3. Solve for :

Background

Topic: Solving Linear Equations

This question tests your ability to solve a linear equation where the variable is multiplied by a constant.

Key Terms and Formulas

• To isolate , divide both sides by $5$.

Step-by-Step Guidance

1. Identify the equation:

2. Divide both sides by $5x$:

3. Simplify both sides:

   (expression to be calculated)

Try solving on your own before revealing the answer!

Q4. Solve for :

Background

Topic: Solving Linear Equations

This question tests your ability to solve a linear equation with both variable and constant terms.

Key Terms and Formulas

• To isolate , first add $7.

Step-by-Step Guidance

1. Identify the equation:

2. Add $7$ to both sides:

3. Simplify:

   (expression to be calculated)

4. Divide both sides by $4x$:

   (expression to be calculated)

Try solving on your own before revealing the answer!

Q5. Solve for :

Background

Topic: Solving Linear Equations with Variables on Both Sides

This question tests your ability to solve a linear equation where appears on both sides.

Key Terms and Formulas

• Move all terms to one side and constants to the other.

Step-by-Step Guidance

1. Identify the equation:

2. Subtract from both sides to get all terms on one side:

3. Simplify:

4. Add $8$ to both sides:

5. Simplify:

   (expression to be calculated)

6. Divide both sides by $3x$:

   (expression to be calculated)

Try solving on your own before revealing the answer!

Q6. Solve for :

Background

Topic: Solving Linear Equations with Multiple Terms

This question tests your ability to combine like terms and solve for .

Key Terms and Formulas

• Combine like terms: Add or subtract terms with the same variable or constant.

Step-by-Step Guidance

1. Identify the equation:

2. Combine like terms on each side:

   Left: ,

   Right:

   So,

3. Subtract from both sides:

4. Simplify:

5. Add $3$ to both sides:

6. Simplify:

Try solving on your own before revealing the answer!

Q7. Solve for :

Background

Topic: Solving Linear Equations with Parentheses

This question tests your ability to use the distributive property and solve for .

Key Terms and Formulas

• Distributive property:

• Combine like terms after distributing.

Step-by-Step Guidance

1. Identify the equation:

2. Apply the distributive property:

   Left: ,

   So,

   Right: ,

   So,

3. Combine like terms:

   Left: , so

   Right: , so

4. Set the simplified equation:

5. Add to both sides:

6. Simplify:

Try solving on your own before revealing the answer!

Q9. Solve for :

Background

Topic: Solving Linear Equations with Fractions

This question tests your ability to solve equations with fractional coefficients and variables on both sides.

Key Terms and Formulas

• Clear fractions by multiplying both sides by the least common denominator (LCD).

• Combine like terms and solve for .

Step-by-Step Guidance

1. Identify the equation:

2. Find the LCD of $5, which is $20$.

3. Multiply both sides by $20$ to clear fractions:

4. Simplify each term:

5. Expand and combine like terms:

6. Subtract from both sides:

7. Simplify:

Try solving on your own before revealing the answer!

Q10. Write an expression for: Five less than four times a number.

Background

Topic: Translating Words to Algebraic Expressions

This question tests your ability to convert a verbal phrase into an algebraic expression.

Key Terms and Formulas

• "Four times a number" means .

• "Five less than" means subtract $5$ from the previous quantity.

Step-by-Step Guidance

1. Identify the number as .

2. Write "four times a number":

3. Subtract $5 to represent "five less than four times a number":

Try writing the expression on your own before revealing the answer!

Q11. The sum of half a number and nine is 15. Find the number.

Background

Topic: Translating Words to Equations and Solving

This question tests your ability to write and solve an equation based on a word problem.

Key Terms and Formulas

• "Half a number" means .

• "Sum" means addition.

Step-by-Step Guidance

1. Let the number be .

2. Write the equation:

3. Subtract $9$ from both sides:

4. Simplify:

5. Multiply both sides by $2x$:

Try solving on your own before revealing the answer!

Q12. Fill in the blank: $0-1$

Background

Topic: Comparing Numbers

This question tests your understanding of inequalities and the order of numbers.

Key Terms and Formulas

• Inequality symbols: (less than), (greater than), (equal to)

Step-by-Step Guidance

1. Compare $0-1$ on the number line.

2. Recall that $0-1$.

3. Choose the correct inequality symbol to fill the blank.

Try filling in the blank on your own before revealing the answer!

Q13. Fill in the blank: ______ $44$

Background

Topic: Comparing Numbers

This question tests your understanding of inequalities and the order of numbers.

Key Terms and Formulas

• Inequality symbols: (less than), (greater than), (equal to)

Step-by-Step Guidance

1. Compare and $44$ on the number line.

2. Recall that is less than $44$.

3. Choose the correct inequality symbol to fill the blank.

Try filling in the blank on your own before revealing the answer!