Unit 4 Test: Equations

The given expression, -4(3w + 7), can be rewritten using the distributive property by multiplying -4 with each term inside the parentheses. This gives us -12w - 28.

The given expression involves combining like terms, which means adding or subtracting terms that have the same variable raised to the same power. In this case, we have 7x and -5x as like terms, which can be combined to give 2x. Similarly, we have 2 and 8 as like terms, which can be combined to give 10. Therefore, the simplified expression is 2x + 10.

The given expression involves combining like terms, which means adding or subtracting terms that have the same variable and exponent. In this case, we have three terms with the variable "w" - "-w", "-5w", and "10w". When we combine these terms, we get 4w. The constant term in the expression is -12. Therefore, the simplified expression is 4w - 12.

To solve the equation 5p - 10 = 0, we need to isolate the variable p. First, we can add 10 to both sides of the equation to get 5p = 10. Then, we divide both sides by 5 to find that p = 2. To check our solution, we substitute p = 2 back into the original equation: 5(2) - 10 = 0. Simplifying this, we get 10 - 10 = 0, which is true. Therefore, the solution is p = 2.

By solving the equation -2x - 6 = 14, we can simplify it by adding 6 to both sides, resulting in -2x = 20. Then, by dividing both sides by -2, we find that x = -10. To check the solution, we substitute x = -10 back into the original equation and see if both sides are equal.

By distributing the 4 to both terms inside the parentheses, we get 8x + 20 = -4. Then, by subtracting 20 from both sides, we have 8x = -24. Finally, dividing both sides by 8, we find that x = -3.

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The given equation is 7x + 4 = 3x. To solve for x, we need to isolate the variable on one side of the equation. By subtracting 3x from both sides, we get 4x + 4 = 0. Then, by subtracting 4 from both sides, we have 4x = -4. Finally, dividing both sides by 4, we find x = -1.

The equation 2x - 3 = 11 matches the statement "The difference of twice a number and three is 11." This equation represents taking twice a number (2x) and subtracting three (-3) from it, resulting in 11.

The equation "x + 6 = 21" matches the statement "The sum of a number and six is 21." This equation represents the sum of a number (x) and six (6) being equal to 21. By subtracting 6 from both sides of the equation, we can solve for x and find that x = 15, which satisfies the given statement.

The correct answer is n n, which simplifies to 12 > n or n

The correct answer is x

Javier saves $15 per week. To save $155, he needs to save for a total of $155 / $15 = 10.33 weeks. Since he cannot save a fraction of a week, he will need to save for 11 weeks. However, the given options do not include 11 weeks. The closest option is 9 weeks, but since Javier has already saved $35, he only needs to save an additional $120. Therefore, it will take him 8 weeks to save enough money.

The given expression is a combination of like terms. By combining the coefficients of the x terms (3x and 5x), we get 8x. Similarly, combining the constant terms (-2 and -7), we get -9. Therefore, the simplified expression is 8x - 9.

The given inequality is -2n > 30. To solve this inequality, we need to isolate n. Dividing both sides of the inequality by -2, we get n

The inequality states that b - 12 is greater than -12. To solve for b, we can add 12 to both sides of the inequality. This gives us b > 0, which means that b is greater than 0.

The graph shows a number line with a shaded region to the right of zero. This indicates that the values of x that satisfy the inequality are greater than or equal to zero. Therefore, the correct answer is x ≥ 0.

The graph shows a number line with an open circle on 4 and an arrow pointing to the right. This indicates that the numbers greater than 4 are included in the solution set. Therefore, the correct inequality represented by the graph is n > 4.

The graph shows a shaded region to the left of the vertical line at x = 2. This means that all the values of x that are less than or equal to 2 are included in the solution. Therefore, the correct inequality represented by the graph is x ≤ 2.

By distributing the -3 to both terms inside the parentheses, the equation becomes -9x + 24 = 2x - 31. By combining like terms, we get -11x = -55. Dividing both sides by -11, we find that x = 5.

The statement "There are more than 30 days in these months" implies that the number of days in these months is greater than 30. In an inequality, the symbol ">" represents "greater than". Therefore, the correct inequality for the statement is "x > 30".

If you have $40 and after buying 6 notebooks you have $4 left, it means you spent $36 on the notebooks. To find the cost of each notebook, divide the total amount spent ($36) by the number of notebooks (6). Therefore, each notebook cost $6.

Lakita is correct in solving the problem because when solving the inequality 8a -7, which means that Lakita correctly solved the problem. Olivia's solution is incorrect because she did not divide both sides by 8.

The inequality x ≤ 8 represents the statement "A number is no more than 8." This is because the symbol "≤" means "less than or equal to," indicating that the number can be equal to 8 or any number less than 8.

The correct answer is n > 12 because the inequality states that n is greater than 12. This means that any value of n that is greater than 12 would satisfy the inequality. To check the solution, we can pick a value greater than 12, such as 13, and substitute it into the inequality. Since 13 is indeed greater than 12, the inequality holds true.