Hard Algebra Worksheets 100 Problems

📆 Updated: 1 Jan 1970
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Algebra worksheets can be a valuable tool for students, providing them with ample practice to strengthen their understanding of this challenging subject. With a diverse range of exercises, these worksheets focus on various algebraic concepts, equipping students with the necessary skills to tackle 100 problems with confidence and proficiency.



Table of Images 👆

  1. 6th Grade Math Worksheets Angles
  2. 2nd Grade Math Word Problems Worksheets
  3. 5th Grade Math Word Problems
  4. 2-Digit Decimal Multiplication Worksheets
  5. Free Printable Math Color by Number Addition Worksheets
  6. 6th Grade Math Coloring Worksheets
  7. Place Value Expanded Form Worksheets
  8. 6th Grade Math Worksheets with Answer Key
6th Grade Math Worksheets Angles
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2nd Grade Math Word Problems Worksheets
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5th Grade Math Word Problems
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2-Digit Decimal Multiplication Worksheets
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Free Printable Math Color by Number Addition Worksheets
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6th Grade Math Coloring Worksheets
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Place Value Expanded Form Worksheets
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6th Grade Math Worksheets with Answer Key
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6th Grade Math Worksheets with Answer Key
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6th Grade Math Worksheets with Answer Key
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6th Grade Math Worksheets with Answer Key
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6th Grade Math Worksheets with Answer Key
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6th Grade Math Worksheets with Answer Key
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6th Grade Math Worksheets with Answer Key
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6th Grade Math Worksheets with Answer Key
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6th Grade Math Worksheets with Answer Key
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6th Grade Math Worksheets with Answer Key
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6th Grade Math Worksheets with Answer Key
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What is the value of x if 3x + 5 = 17?

The value of x is 4. This can be found by isolating x in the equation 3x + 5 = 17. Subtracting 5 from both sides gives 3x = 12, and then dividing by 3 gives x = 4.

Solve the equation 2(4x + 3) = 10x - 6.

To solve the equation 2(4x + 3) = 10x - 6, first distribute the 2 on the left side: 8x + 6 = 10x - 6. Then, move all the terms with x to one side by subtracting 8x from both sides: 6 = 2x - 6. Next, add 6 to both sides: 12 = 2x. Finally, divide by 2 to solve for x: x = 6.

Simplify the expression 5(2x - 3) - 4(x + 2).

To simplify the expression 5(2x - 3) - 4(x + 2), first distribute the 5 and 4 to the terms inside the parentheses: 10x - 15 - 4x - 8. Then, combine like terms to simplify further: 10x - 4x - 15 - 8 = 6x - 23. Thus, the simplified expression is 6x - 23.

Find the roots of the quadratic equation x^2 + 6x - 7 = 0.

To find the roots of the quadratic equation x^2 + 6x - 7 = 0, we can use the quadratic formula: x = (-b ± ?(b^2 - 4ac)) / 2a. Here, a = 1, b = 6, and c = -7. By substituting these values into the formula, we get x = (-6 ± ?(6^2 - 4*1*(-7))) / 2*1. Simplifying this further, x = (-6 ± ?(36 + 28)) / 2, x = (-6 ± ?64) / 2, x = (-6 ± 8) / 2. Therefore, the roots are x = (-6 + 8) / 2 and x = (-6 - 8) / 2, which simplifies to x = 1 and x = -7. The roots of the quadratic equation x^2 + 6x - 7 = 0 are x = 1 and x = -7.

Simplify the expression (2x^3 - 3x^2 + x) + (4x^2 + 5x - 2).

The simplified expression is 2x^3 + x + x^2 + 5x - 2.

Solve the equation 3(2y + 1) - 4(y - 3) = 8y - 5.

To solve the equation 3(2y + 1) - 4(y - 3) = 8y - 5, we need to first distribute the terms inside the parentheses. This gives us 6y + 3 - 4y + 12 = 8y - 5. Simplifying further, we combine like terms to get 2y + 15 = 8y - 5. Next, we isolate the variable terms on one side, so subtract 2y from both sides to get 15 = 6y - 5. Adding 5 to both sides, we have 20 = 6y. Finally, divide by 6 to solve for y, giving us y = 20/6 or y = 10/3.

Factor the expression 9x^2 - 24x + 16.

To factor the expression 9x^2 - 24x + 16, we first look for two numbers that multiply to 9*16=144 and add up to -24. The numbers that fit this criteria are -12 and -12. Therefore, the factored form of 9x^2 - 24x + 16 is (3x - 4)^2.

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

To solve the system of equations 2x + 3y = 4 and 4x - 2y = 10, we can first multiply the first equation by 2 to get 4x + 6y = 8. Then, we can add the two equations together to eliminate the y variable: 4x + 6y + 4x - 2y = 8 + 10, which simplifies to 8x + 4 = 18. Solve for x by isolating x: 8x = 14, x = 14/8 = 7/4 or 1.75. Substitute x back into either equation, like 2x + 3y = 4, to solve for y: 2(1.75) + 3y = 4, 3.5 + 3y = 4, 3y = 0.5, y = 0.5/3 = 1/6 or approximately 0.167. Therefore, the solution to the system of equations is x = 1.75 and y = 0.167.

Simplify the expression (a^2 - b^2)/(a^2 + 2ab + b^2).

The expression can be simplified to (a - b)/(a + b).

Find the value of y if (3y + 2)^2 = 49.

To find the value of y, we can first expand the expression (3y + 2)^2 as (3y + 2)(3y + 2) = 3y(3y) + 2(3y) + 3y(2) + 2(2) = 9y^2 + 6y + 6y + 4 = 9y^2 + 12y + 4. Now, we set this equal to 49: 9y^2 + 12y + 4 = 49. Simplifying further, we get 9y^2 + 12y - 45 = 0. Factoring this quadratic equation, we have (3y + 15)(3y - 3) = 0, which gives us y = -5 or y = 1. Thus, the values of y are -5 and 1.

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