Pre-Algebra Worksheet Answers

Are you a pre-algebra student in search of detailed and reliable answers for your worksheets? Look no further! We understand that understanding and mastering pre-algebra concepts can sometimes be challenging. That's why we have compiled a collection of pre-algebra worksheet answers to help you strengthen your understanding of this subject.

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What is the solution to the equation 2x + 5 = 13?

The solution to the equation 2x + 5 = 13 is x = 4. By isolating the variable x, we can subtract 5 from both sides of the equation to get 2x = 8, and then divide by 2 to find x = 4.

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

To simplify the expression 3(2x - 4) - 5x, first distribute the 3 to both terms inside the parentheses: 3*2x = 6x and 3*(-4) = -12. Then the expression becomes 6x - 12 - 5x. Combining like terms gives us the simplified form: 6x - 5x - 12 = x - 12. Therefore, the simplified expression is x - 12.

Solve for x in the equation 5(x - 12) + 3 = 2(x + 10) - 7.

To solve for x in the equation 5(x - 12) + 3 = 2(x + 10) - 7, first distribute and simplify both sides. This gives us 5x - 60 + 3 = 2x + 20 - 7. Combining like terms results in 5x - 57 = 2x + 13. Next, subtract 2x from both sides to get 3x - 57 = 13. Then, add 57 to both sides to obtain 3x = 70. Finally, divide by 3 on both sides to find x = 70 / 3, simplifying to x = 23.

Find the value of y if 3y - 7 = 5y + 1.

To find the value of y, we can solve the given equation. By rearranging the terms, we get 3y - 5y = 1 + 7, which simplifies to -2y = 8. Dividing both sides by -2 gives us y = -4. Therefore, the value of y is -4.

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

The simplified expression is 6x^2 - 3x + 7.

Solve the inequality 2x - 5 ? 7.

To solve the inequality 2x - 5 ? 7, we first add 5 to both sides to get 2x ? 12. Then, we divide by 2 to isolate x, yielding x ? 6. Therefore, the solution to the inequality is x ? 6.

Determine the slope of the line passing through the points (3, -2) and (-1, 4).

To determine the slope of the line passing through two points, we can use the formula for slope, which is given by (y2 - y1) / (x2 - x1), where (x1, y1) = (3, -2) and (x2, y2) = (-1, 4). Substituting the values into the formula, we get (4 - (-2)) / (-1 - 3) = 6 / -4 = -3/2. Therefore, the slope of the line passing through the points (3, -2) and (-1, 4) is -3/2.

Find the midpoint of the line segment with endpoints (2, -3) and (6, 1).

To find the midpoint of a line segment, you average the x-coordinates and y-coordinates of the endpoints. In this case, the midpoint will be (4, -1).

Factor the expression 4x^2 - 9.

The expression 4x^2 - 9 can be factored into the difference of squares as (2x + 3)(2x - 3).

Solve the system of equations: 2x + y = 5 and x - y = 3.

To solve the system of equations 2x + y = 5 and x - y = 3, we can solve for y in the second equation, which gives y = x - 3. Substituting this value of y into the first equation, we get 2x + x - 3 = 5, simplifying to 3x - 3 = 5, and then 3x = 8, which gives x = 8/3. Substituting x back into the second equation x - y = 3, we get 8/3 - y = 3, simplifying to y = 8/3 - 3 = -1/3. Therefore, the solution to the system of equations is x = 8/3 and y = -1/3.