Basic Algebra Problems Worksheet
Are you a high school student who wants to sharpen your algebra skills? Look no further! We have curated a comprehensive Basic Algebra Problems Worksheet that focuses on entity and subject, allowing you to practice various mathematical concepts at your own pace.
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What is the value of x in the equation 3x + 5 = 17?
The value of x in the equation 3x + 5 = 17 is x = 4. This can be found by subtracting 5 from both sides of the equation to isolate 3x, then dividing both sides by 3 to solve for x.
Simplify the expression 4x^2 + 2x - 8.
The expression 4x^2 + 2x - 8 can be simplified as 2(2x^2 + x - 4).
Solve the system of equations: 2x - 3y = 10 and x + y = 7.
By using the second equation x + y = 7, we can express y as y = 7 - x. Substituting this expression into the first equation 2x - 3y = 10 yields 2x - 3(7 - x) = 10. Simplifying this gives 2x - 21 + 3x = 10, which simplifies further to 5x = 31. Solving for x gives x = 31/5. Substituting x back into y = 7 - x gives y = 7 - 31/5, so y = 8/5. Therefore, the solution to the system of equations is x = 31/5 and y = 8/5.
Factor the expression x^2 + 5x + 6.
The expression x^2 + 5x + 6 factors into (x + 2)(x + 3).
Solve the inequality 2x - 3 > 9.
To solve the inequality 2x - 3 > 9, first add 3 to both sides to isolate the variable: 2x > 12. Then, divide by 2 on both sides to find the value of x: x > 6. Therefore, the solution to the inequality is x is greater than 6.
Determine the slope of the line represented by the equation 2x + 3y = 9.
To determine the slope of the line, we need to rewrite the equation in slope-intercept form, y = mx + b, where m is the slope. By isolating y in the equation 2x + 3y = 9, we get y = (-2/3)x + 3. Therefore, the slope is -2/3.
Solve the equation 5(x - 2) + 3 = 2x - 5.
To solve the equation 5(x - 2) + 3 = 2x - 5, we first distribute the 5 to both terms inside the parentheses: 5x - 10 + 3 = 2x - 5. Next, combine like terms on both sides of the equation: 5x - 7 = 2x - 5. Then, move the 2x term to the left side by subtracting it from both sides: 3x - 7 = -5. Finally, isolate the variable by adding 7 to both sides: 3x = 2. Dividing by 3 on both sides gives the solution x = 2/3.
Simplify the expression (2x + 4)(x - 3).
To simplify the expression (2x + 4)(x - 3), you can use the distributive property to multiply each term in the first expression by each term in the second expression. This gives you (2x * x) + (2x * -3) + (4 * x) + (4 * -3), which simplifies to 2x^2 - 6x + 4x - 12. Combining like terms, the expression simplifies to 2x^2 - 2x - 12.
Find the domain of the function f(x) = ?(3x + 2).
The function f(x) = ?(3x + 2) is defined for real numbers that make the radicand (3x + 2) non-negative. This means that 3x + 2 ? 0. Solving for x gives x ? -2/3. Therefore, the domain of the function f(x) = ?(3x + 2) is all real numbers greater than or equal to -2/3, or in interval notation, [-2/3, ?).
Solve the quadratic equation x^2 - 6x + 8 = 0.
To solve the quadratic equation x^2 - 6x + 8 = 0, you can factor it as (x - 4)(x - 2) = 0, which means x = 4 or x = 2 are the solutions to the equation.
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