Q1. Solve the equation: 0.6(x + 8) - 0.2(x - 0.3) = 15.26

Background

Topic: Linear Equations

This question tests your ability to solve linear equations with variables on both sides, including distributing and combining like terms.

Key Terms and Formulas

• Distributive Property:

• Combining like terms: Add or subtract coefficients of the same variable.

Step-by-Step Guidance

1. Distribute to and to .

2. Write out the equation after distribution: .

3. Combine like terms ( and ).

4. Isolate the variable term on one side by subtracting the constant from both sides.

Try solving on your own before revealing the answer!

Q2. Solve the equation: (4x - 1)/2 = (x - 4)/3

Background

Topic: Linear Equations with Fractions

This question tests your ability to solve equations involving fractions by clearing denominators.

Key Terms and Formulas

• Multiplying both sides by the least common denominator (LCD) to eliminate fractions.

Step-by-Step Guidance

1. Identify the denominators: $2. The LCD is $6$.

2. Multiply both sides of the equation by $6$ to clear the fractions.

3. Simplify both sides and combine like terms.

4. Isolate and solve for it.

Try solving on your own before revealing the answer!

Q3. Solve the equation: (x/9) - (4/x) = 2/3

Background

Topic: Rational Equations

This question tests your ability to solve equations with variables in the denominator by finding a common denominator and clearing fractions.

Key Terms and Formulas

• Multiplying both sides by the least common denominator (LCD) to eliminate fractions.

Step-by-Step Guidance

1. Identify the denominators: $9x. The LCD is .

2. Multiply both sides by to clear the denominators.

3. Simplify each term and combine like terms.

4. Isolate and solve for it.

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Q4. The total length of three steel pieces, A, B, and C, is 57 feet. Steel B is twice as long as steel A, and steel C is one foot more than five times the length of steel A. Find the length of each steel piece.

Background

Topic: Systems of Linear Equations / Word Problems

This question tests your ability to translate a word problem into an equation and solve for unknowns.

Key Terms and Formulas

• Let = length of steel A.

• Steel B =

• Steel C =

• Total length:

Step-by-Step Guidance

1. Write expressions for each steel piece in terms of .

2. Set up the equation: .

3. Combine like terms to simplify the equation.

4. Isolate and solve for it.

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Q5. Find the perimeter and area of a room whose length is 14 feet and width is 9 feet.

Background

Topic: Perimeter and Area of Rectangles

This question tests your ability to use formulas for perimeter and area of rectangles.

Key Terms and Formulas

• Perimeter:

• Area:

• = length, = width

Step-by-Step Guidance

1. Identify the length ( ft) and width ( ft).

2. Plug the values into the perimeter formula: .

3. Plug the values into the area formula: .

4. Simplify each expression to find the perimeter and area.

Try solving on your own before revealing the answer!