Long Algebra Problems Worksheet
Are you searching for a comprehensive worksheet to help your middle or high school students practice their algebra skills? Look no further! Introducing our long algebra problems worksheet, designed to provide ample practice for students struggling with complex equations and expressions. With a focus on entities and subjects, this worksheet is perfect for educators looking to reinforce algebra concepts in a clear and structured manner. Available for download, this resource will surely benefit both teachers and students alike.
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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.
Expand the expression (a - b)^2.
The expansion of the expression (a - b)^2 is a^2 - 2ab + b^2.
Solve the system of equations: 2x + 3y = 10 and 4x - y = 7.
To solve the system of equations, we can first isolate y in the second equation: y = 4x - 7. Then we substitute this expression for y into the first equation: 2x + 3(4x - 7) = 10. Simplifying this equation gives us: 2x + 12x - 21 = 10, which becomes 14x = 31, finally yielding x = 31/14. Substituting x back into the second equation to solve for y: 4(31/14) - y = 7, which simplifies to y = 31/14 + 28/14 = 59/14. Therefore, the solution to the system of equations is x = 31/14 and y = 59/14.
Simplify the expression 4x^2 + 7x - 3x^2 + 2x - 6.
This expression simplifies to x^2 + 9x - 6.
Solve the quadratic equation x^2 - 5x + 6 = 0.
To solve the quadratic equation x^2 - 5x + 6 = 0, you can factor it into (x - 2)(x - 3) = 0. This gives two solutions: x = 2 and x = 3.
Factor the expression 4x^2 - 12x + 9.
The expression 4x^2 - 12x + 9 can be factored into (2x - 3)(2x - 3), or more simply, (2x - 3)^2.
Simplify the expression (2x^3)^2 ÷ (3x)^4.
To simplify the expression \((2x^3)^2 ÷ (3x)^4\), first square the term inside the parenthesis to get \(4x^6\), and raise the term \(3x\) to the 4th power to get \(81x^4\). Then, divide \(4x^6\) by \(81x^4\) to simplify the expression, which gives the result \(\frac{4}{81}x^2\).
Solve the equation log(x) + log(x + 2) = 3.
To solve the equation log(x) + log(x + 2) = 3, we can combine the two logarithms using the product rule of logarithms, which states that log(a) + log(b) = log(ab). Therefore, the equation simplifies to log(x(x + 2)) = 3. Next, we can rewrite this in exponential form as 10^3 = x(x + 2). Solving for x gives us x = 8.
Find the midpoint between the points (3, 5) and (-2, 7).
To find the midpoint between two points (x?, y?) and (x?, y?), you can use the midpoint formula: ((x? + x?) / 2, (y? + y?) / 2). Applying this to the given points (3, 5) and (-2, 7), the midpoint would be ((3 + (-2)) / 2, (5 + 7) / 2) which simplifies to (0.5, 6). Therefore, the midpoint between the points (3, 5) and (-2, 7) is (0.5, 6).
Solve the equation 2^(x+1) = 16.
To solve the equation 2^(x+1) = 16, we first need to rewrite 16 as a power of 2, which is 2^4. Therefore, the equation becomes 2^(x+1) = 2^4. Since the bases are the same, we can set the exponents equal to each other: x + 1 = 4. Solving for x gives x = 3. Hence, the solution to the equation 2^(x+1) = 16 is x = 3.
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