Pre-Algebra Pretest Practice Quiz for Success

By combining like terms, you add the coefficients 3 and 2 to obtain 5, resulting in 5x. This process is a basic step in simplifying algebraic expressions.

Subtracting 4 from both sides of the equation gives x = 5. This straightforward approach is fundamental to solving linear equations.

Substitute x = 2 into the expression to get 2(2 + 3) which simplifies to 2 � - 5 = 10. This exercise reinforces the method of substitution in algebra.

The slope-intercept form of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept. This form is especially useful for quickly graphing linear equations.

Dividing 12 by 3 gives 4. This simple arithmetic operation is essential for building confidence in solving algebraic problems.

Add 3 to both sides to obtain 2x = 8, then divide by 2 to find x = 4. This method of isolating the variable is a common strategy in solving linear equations.

Distribute 3 to get 3x - 6 = 12, then add 6 to both sides and divide by 3 to determine x = 6. This question tests your understanding of the distributive property and solving equations.

Combine like terms: 4x - 2x results in 2x and 5 + 3 results in 8, giving the simplified expression 2x + 8. Combining like terms is crucial in simplifying any algebraic expression.

Subtract 2x from both sides to obtain 3x + 7 = 16, then subtract 7 to get 3x = 9 and finally divide by 3 to find x = 3. This problem reinforces the technique of isolating variables.

In the slope-intercept form y = mx + b, the coefficient m is the slope of the line. Here, m is -3, indicating the line falls as x increases.

Rewriting 2(x + 4) as 2x + 8 uses the distributive property, which allows you to multiply a single term by each term inside the parentheses. This property is essential in simplifying expressions.

Subtracting 3 from both sides results in x > 4. This question emphasizes the similarity between solving equations and inequalities.

First, distribute -2 to get -2 + 2x, then combine with 3x to obtain 5x - 2. This demonstrates correct use of the distributive property and combining like terms.

Distribute -3 across (2x - 4) to obtain -6x + 12 and then combine with 2x to get -4x + 12. This exercise tests both the distributive property and combining like terms.

Expanding the left side of the equation gives 2x + 2. Subtracting x from both sides results in x + 2 = 7, so x = 5 after subtracting 2. This problem reinforces the process of isolating the variable.

Multiplying every term by 6, the least common multiple of 3 and 2, clears the fractions. After simplifying and isolating x, the solution is x = 12.

Adding the two equations gives 2x = 12, so x = 6; substituting back into one of the equations gives y = 4. This method of elimination is effective for solving systems of linear equations.

x² - 9 is recognized as a difference of two squares, which factors as (x - 3)(x + 3). This factorization strategy is a key skill in algebra.

In vertex form, y = a(x - h)² + k, the vertex is (h, k). Therefore, the x-coordinate of the vertex is 3. The positive coefficient indicates the parabola opens upward.

To compute f(g(x)), substitute g(x) into f(x) to get 3(x - 5) + 2, which simplifies to 3x - 15 + 2 and ultimately to 3x - 13. This exercise tests your understanding of function composition.