Create Study Quiz: Your Ultimate Practice Test

Subtracting 5 from both sides of the equation gives x = 4. This demonstrates the basic principle of isolating the variable by performing the same operation on both sides.

The constant term in an expression is the number without any attached variable. Here, 4 is the constant term because it stands alone without a variable.

Since 2x and 3x are like terms, you add their coefficients to get 5x. This is a fundamental example of combining like terms in algebra.

The expression y + 7 correctly shows that 7 is added to the variable y. The other options do not represent the operation of addition with y as intended.

By substituting x with 2, the expression 3x becomes 3 * 2, which equals 6. This simple substitution exercise reinforces understanding of variable evaluation.

Adding 4 to both sides gives 3x = 15, and then dividing both sides by 3 results in x = 5. This problem reinforces the steps involved in solving linear equations.

First, use the distributive property to expand 2(x + 5) into 2x + 10. Subtracting x from 2x gives x, leading to the simplified form x + 10.

Substitute 7 for a to calculate 4(7) - 3, which simplifies to 28 - 3 = 25. This exercise focuses on the proper substitution of a value into an algebraic expression.

Using the distributive property, multiply 3 by both x and 4 to get 3x + 12. This effectively expands the original expression.

Multiply both sides of the equation by 2 to obtain 5x = 20, and then divide by 5 to solve for x, resulting in x = 4. This problem demonstrates solving an equation that involves a fraction.

Subtracting 3 from both sides of the equation gives 2y = 4, and then dividing by 2 yields y = 2. This is a straightforward linear equation solving exercise.

Combine the like terms by subtracting x from 2x to get x, and add the constants 3 and 5 to get 8, resulting in x + 8. This question reinforces the process of combining like terms.

Adding the coefficients of terms that have the same variable is known as combining like terms. This is a key technique in simplifying algebraic expressions.

Distribute the 2 to get 2x - 6, then add 6 to both sides to obtain 2x = 16, and finally divide by 2 to find x = 8. This exercise tests both the distributive property and solving linear equations.

Substitute x with 3 in the function f(x) to get f(3) = 2(3) + 1, which simplifies to 7. This question reinforces evaluating functions by substitution.

Subtract 2 from both sides to obtain x/3 = 3 and then multiply both sides by 3 to solve for x, resulting in x = 9. This exercise requires managing fractions and basic arithmetic operations.

First, distribute the 3 on the left-hand side to obtain 3x + 6. Then, subtract 2x from both sides and subtract 6 to isolate x, which results in x = 6.

The equation from the word problem is 5x - 4 = 21. Adding 4 to both sides gives 5x = 25, and dividing by 5 results in x = 5.

Multiply both sides by the least common multiple of 3 and 2 (which is 6) to eliminate the fractions, resulting in 2(2x - 1) = 3(x + 5). Solving the resulting equation gives x = 17.

Expanding 2(x + a) results in 2x + 2a. Equating this to 2x + 14 and subtracting 2x from both sides leaves 2a = 14, so dividing by 2 gives a = 7.