7th Grade Algebra Homework - Dec 11, 12:23

Solution

Correct: B

To solve for x, you need to isolate x on one side of the equation. Since 8 is being added to x, you subtract 8 from both sides of the equation: x + 8 - 8 = 20 - 8 x = 12 So, the value of x is 12.

Solution

Correct: B

To solve for y, you need to isolate y. Since y is being multiplied by 4, you divide both sides of the equation by 4: 4y / 4 = 28 / 4 y = 7 So, the value of y is 7.

Solution

Correct: B

This is a two-step equation. Step 1: Get rid of the constant term on the side with the variable. Since 7 is being subtracted from 3m, add 7 to both sides: 3m - 7 + 7 = 14 + 7 3m = 21 Step 2: Isolate m. Since m is being multiplied by 3, divide both sides by 3: 3m / 3 = 21 / 3 m = 7 So, the value of m is 7.

Solution

Correct: A

To simplify the expression, combine like terms. Like terms have the same variable raised to the same power. Group the 'a' terms: 5a - 2a = (5 - 2)a = 3a Group the 'b' terms: 3b + b = 3b + 1b = (3 + 1)b = 4b Combine the simplified terms: 3a + 4b So, the simplified expression is 3a + 4b.

Solution

Correct: C

The distributive property states that a(b + c) = ab + ac. In this case, 'a' is 4, 'b' is x, and 'c' is -3. Multiply 4 by x: 4 * x = 4x Multiply 4 by -3: 4 * (-3) = -12 Combine the results: 4x - 12 So, the expanded expression is 4x - 12.

Solution

Correct: B

To evaluate the expression, substitute the given values for p and q into the expression. Substitute p = 5: 3(5) - 2q = 15 - 2q Substitute q = 2: 15 - 2(2) = 15 - 4 Calculate the final result: 15 - 4 = 11 So, the value of the expression is 11.

Solution

Correct: B

Let 'n' represent the number. 'The sum of a number and 6' means n + 6. 'Divided by 2' means that the entire sum (n + 6) is divided by 2. To ensure the entire sum is divided, it must be enclosed in parentheses. So, the expression is (n + 6) / 2.

Solution

Correct: D

To solve the inequality, isolate x. Add 4 to both sides: x - 4 + 4 > 7 + 4 x > 11 This means x must be a number greater than 11. Out of the given choices, only 12 is greater than 11.

Solution

Correct: B

To solve for x, you need to isolate x. Since 1.5 is being added to x, subtract 1.5 from both sides of the equation: x + 1.5 - 1.5 = 4.0 - 1.5 x = 2.5 So, the value of x is 2.5.

Solution

Correct: B

First, find the total cost of 's' shirts. If one shirt costs 15 dollars, 's' shirts will cost 15 * s, or 15s dollars. To find the change received, you subtract the total cost of the shirts from the amount you paid. Amount paid: 50 dollars Total cost of shirts: 15s dollars Change = Amount paid - Total cost = 50 - 15s So, the expression for the change you receive is 50 - 15s.