8th Grade Algebra Problems Worksheet
Are you searching for a resource that will help reinforce your understanding of algebra concepts? Look no further! Our 8th Grade Algebra Problems Worksheet is designed to provide targeted practice for students in this grade level. With a variety of problems covering various topics, this worksheet will help you solidify your understanding of algebraic concepts and enhance your problem-solving skills.
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What is the formula for calculating the slope of a line?
The formula for calculating the slope of a line is given by the difference in the y-coordinates divided by the difference in the x-coordinates of any two points on the line. Mathematically, it is represented as: Slope (m) = (y2 - y1) / (x2 - x1).
Solve the equation 2x + 5 = 15.
To solve the equation 2x + 5 = 15, first subtract 5 from both sides to isolate the variable. This gives us 2x = 10. Next, divide both sides by 2 to solve for x, which gives x = 5. Therefore, the solution to the equation is x = 5.
What are the steps to factorize a quadratic equation?
To factorize a quadratic equation, you first need to determine if the equation can be factored. Then, multiply the coefficient of the squared term by the constant term. Find two numbers that multiply to this result and add up to the coefficient of the linear term. Use these numbers to rewrite the middle term of the quadratic equation as a sum. Next, factor the quadratic equation using the technique of grouping or the quadratic formula as needed. Finally, simplify the factors to get the final factored form of the quadratic equation.
Find the value of x in the equation 3(x - 4) = 8 - 2x.
To find the value of x in the equation 3(x - 4) = 8 - 2x, you need to first distribute the 3 on the left side of the equation, which will give you 3x - 12. Then, simplify the equation by combining like terms on both sides, which will lead to 3x - 12 = 8 - 2x. Next, add 2x to both sides to get 5x - 12 = 8. After that, add 12 to both sides, resulting in 5x = 20. Finally, solve for x by dividing both sides by 5, giving you x = 4. Thus, the value of x in the equation is 4.
How do you solve a system of linear equations using substitution?
To solve a system of linear equations using substitution, you first isolate one variable in one of the equations. Then, substitute the expression for that variable into the other equation. This will create a new equation with only one variable, which can be solved to find its value. Once you have found the value of one variable, you can substitute it back into one of the original equations to solve for the other variable. This process allows you to find the values of both variables and ultimately solve the system of linear equations.
Simplify the expression 3x^2 + 2x - 5x + 4.
The expression 3x^2 + 2x - 5x + 4 simplifies to 3x^2 - 3x + 4.
What is the concept of absolute value and how is it represented in equations?
Absolute value is a mathematical concept that represents the distance of a number from zero on a number line, without considering its sign. It is denoted by vertical bars surrounding the number, such as |x|. In equations, the absolute value function is often used to ensure that a value is positive, as it removes the negative sign of a number if it is present. For example, in the equation |x| = 5, the absolute value of x is 5, so x can be either 5 or -5.
Solve the inequality 4x - 8 ? 20.
To solve the inequality 4x - 8 ? 20, first, add 8 to both sides to isolate the x-term. This gives you 4x ? 28. Then, divide by 4 on both sides to solve for x, which gives x ? 7. Therefore, the solution to the inequality is x is less than or equal to 7.
How do you find the average rate of change in a linear function?
To find the average rate of change in a linear function, you subtract the y-values of two different points on the function to find the change in y, and subtract the x-values of the same two points to find the change in x. Then, divide the change in y by the change in x to calculate the average rate of change. This represents how much the function is changing on average as x changes from one point to another.
Solve the equation 3/4(x + 2) + 2 = 3x - 1/2.
To solve the equation 3/4(x + 2) + 2 = 3x - 1/2, first distribute the 3/4 on the left side: 3/4 * x + 3/4 * 2 + 2 = 3x - 1/2. This simplifies to 3x/4 + 3/2 + 2 = 3x - 1/2. Then combine like terms on the left side to get 3x/4 + 7/2 = 3x - 1/2. Next, subtract 3x from both sides to get 3x/4 - 3x + 7/2 = -1/2. To eliminate fractions, multiply all terms by 4 to get 3x - 12x + 14 = -2. Simplify to get -9x + 14 = -2. Now, subtract 14 from both sides to get -9x = -16. Finally, divide by -9 to solve for x and get x = 16/9.
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