Basic Algebra Worksheets 5th Grade

Are you searching for a comprehensive and engaging resource to help your 5th grade students master basic algebra concepts? Look no further than our collection of Basic Algebra Worksheets specifically designed for 5th graders. These worksheets provide the perfect balance of challenge and support, making them ideal for introducing new topics or reinforcing existing knowledge. With clear instructions and a range of practice problems, our worksheets ensure that students become confident in solving algebraic equations and understanding the core principles of algebra.

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What is the value of x in the equation 3x + 5 = 20?

The value of x in the equation 3x + 5 = 20 is x = 5.

Solve the equation 4y - 8 = 12 for y.

To solve the equation 4y - 8 = 12 for y, first add 8 to both sides to isolate 4y. This gives 4y = 20. Then, divide both sides by 4 to solve for y. Therefore, y = 5. So the solution to the equation is y = 5.

How would you simplify the expression 2(3 + 5) - 4?

To simplify the expression 2(3 + 5) - 4, first solve the parentheses 3 + 5 which equals 8. Then multiply 2 by 8 to get 16. Finally, subtract 4 from 16 to get the final result of 12.

Find the sum of 2x + 3 and 4x - 1.

The sum of 2x + 3 and 4x - 1 is 6x + 2.

Expand the expression (2a - 3b)(4a + 5b).

To expand the expression (2a - 3b)(4a + 5b), you multiply each term of the first expression (2a - 3b) by each term of the second expression (4a + 5b) and then combine like terms. This results in 8a^2 + 10ab - 12ab - 15b^2, which simplifies to 8a^2 - 2ab - 15b^2.

Factorize the expression 6x^2 - 9x.

To factorize the expression 6x^2 - 9x, we can first factor out the greatest common factor, which is 3x. So, the expression becomes 3x(2x - 3). Therefore, 6x^2 - 9x can be factorized as 3x(2x - 3).

Evaluate the expression 2x^3 + 3y^2 when x = 2 and y = 1.

Substitute x = 2 and y = 1 into the expression 2x^3 + 3y^2: 2(2)^3 + 3(1)^2 = 2(8) + 3(1) = 16 + 3 = 19. Therefore, the value of the expression 2x^3 + 3y^2 when x = 2 and y = 1 is 19.

Solve the inequality 4x + 3 < 15 for x.

To solve the inequality 4x + 3 < 15 for x, first subtract 3 from both sides to isolate the 4x term: 4x < 12. Then divide by 4 on both sides to solve for x, which gives x < 3. Therefore, the solution to the inequality is x is less than 3.

Given the function f(x) = 2x + 3, find f(5).

To find f(5), substitute x with 5 in the function f(x) = 2x + 3. Thus, f(5) = 2(5) + 3 = 10 + 3 = 13. Therefore, f(5) = 13.

Solve the system of equations: 3x + 2y = 10 and 2x - y = 4.

To solve the system of equations 3x + 2y = 10 and 2x - y = 4, we can use the substitution method. From the second equation, we can express y in terms of x as y = 2x - 4. Substitute this into the first equation: 3x + 2(2x - 4) = 10. Simplifying gives 3x + 4x - 8 = 10, which further simplifies to 7x = 18. Therefore, x = 18/7. Substitute x back into y = 2x - 4 to find y. Thus, y = 2(18/7) - 4 = 36/7 - 4 = 20/7. Therefore, the solution to the system of equations is x = 18/7 and y = 20/7.