Solving Equations With Multiple Variables

1) Solve for h: 15 = 3h + 4

H = 11/3

H = 3

H = 4

H = 19/3

To solve for \( h \) in the equation \( 15 = 3h + 4 \), first subtract 4 from both sides to isolate the term with \( h \): \( 15 - 4 = 3h \), which simplifies to \( 11 = 3h \). Next, divide both sides by 3 to solve for \( h \): \( h = \frac{11}{3} \). This fraction represents the value of \( h \) that satisfies the original equation.

Explanation

To solve for \( h \) in the equation \( 15 = 3h + 4 \), first subtract 4 from both sides to isolate the term with \( h \): \( 15 - 4 = 3h \), which simplifies to \( 11 = 3h \). Next, divide both sides by 3 to solve for \( h \): \( h = \frac{11}{3} \). This fraction represents the value of \( h \) that satisfies the original equation.

2) Solve for h: A = bh

H = A + b

H = A/b

H = b/A

H = Ab

To solve for h in the equation A = bh, we need to isolate h. We can do this by dividing both sides of the equation by b. This gives us h = A/b, which expresses h as a function of A and b. The other options do not correctly isolate h based on the original equation.

Explanation

To solve for h in the equation A = bh, we need to isolate h. We can do this by dividing both sides of the equation by b. This gives us h = A/b, which expresses h as a function of A and b. The other options do not correctly isolate h based on the original equation.

3) Solve for h: S = 2B + 4h

H = (S + 2B) / 4

H = (S - 2B) / 4

H = S - 2B

H = (2B - S) / 4

To isolate h in the equation S = 2B + 4h, we first subtract 2B from both sides, yielding S - 2B = 4h. Next, we divide both sides by 4 to solve for h, resulting in h = (S - 2B) / 4. This transformation maintains the equality and correctly expresses h in terms of S and B.

Explanation

To isolate h in the equation S = 2B + 4h, we first subtract 2B from both sides, yielding S - 2B = 4h. Next, we divide both sides by 4 to solve for h, resulting in h = (S - 2B) / 4. This transformation maintains the equality and correctly expresses h in terms of S and B.

4) Solve for h: W = Bh/3

H = 3W/B

H = W/(3B)

H = 3B/W

H = BW/3

To solve for \( h \) in the equation \( W = \frac{Bh}{3} \), we need to isolate \( h \). Start by multiplying both sides by 3 to eliminate the fraction, resulting in \( 3W = Bh \). Next, divide both sides by \( B \) to isolate \( h \), yielding \( h = \frac{3W}{B} \). This manipulation shows how to rearrange the equation step-by-step, leading to the final expression for \( h \).

Explanation

To solve for \( h \) in the equation \( W = \frac{Bh}{3} \), we need to isolate \( h \). Start by multiplying both sides by 3 to eliminate the fraction, resulting in \( 3W = Bh \). Next, divide both sides by \( B \) to isolate \( h \), yielding \( h = \frac{3W}{B} \). This manipulation shows how to rearrange the equation step-by-step, leading to the final expression for \( h \).

5) What error did Student A make when solving 8x + 2y = 100 for x?

Student A subtracted 2y instead of dividing by 8

Student A subtracted 8 instead of dividing by 8

Student A added 2y to both sides

Student A multiplied both sides by 8

In solving the equation 8x + 2y = 100 for x, Student A made a mistake by subtracting 8 instead of dividing the entire equation by 8 to isolate x. The correct approach involves first moving the 2y term to the other side by subtracting it, and then dividing the resulting equation by 8 to solve for x. By incorrectly subtracting 8, Student A failed to properly manipulate the equation, leading to an incorrect solution.

Explanation

In solving the equation 8x + 2y = 100 for x, Student A made a mistake by subtracting 8 instead of dividing the entire equation by 8 to isolate x. The correct approach involves first moving the 2y term to the other side by subtracting it, and then dividing the resulting equation by 8 to solve for x. By incorrectly subtracting 8, Student A failed to properly manipulate the equation, leading to an incorrect solution.

6) What error did Student B make when solving 8x + 2y = 100 for x?

Student B forgot to subtract 2y

Student B divided only 100 by 8 but did not divide -2y by 8

Student B multiplied both sides by 2

Student B added 8 to both sides

Student B's error occurred during the process of isolating x in the equation 8x + 2y = 100. When attempting to solve for x, it is crucial to perform the same operation on all terms. By dividing only the constant term (100) by 8 and neglecting to divide the -2y term by 8, Student B failed to maintain the equality of the equation, leading to an incorrect solution for x. Properly dividing all terms by 8 would have yielded the correct value for x.

Explanation

Student B's error occurred during the process of isolating x in the equation 8x + 2y = 100. When attempting to solve for x, it is crucial to perform the same operation on all terms. By dividing only the constant term (100) by 8 and neglecting to divide the -2y term by 8, Student B failed to maintain the equality of the equation, leading to an incorrect solution for x. Properly dividing all terms by 8 would have yielded the correct value for x.

7) What is the correct solution for x when solving 8x + 2y = 100?

X = 92 - 2y

X = 12.5 - 2y

X = 12.5 - 0.25y

X = 100 - 2y

To isolate x in the equation 8x + 2y = 100, we first subtract 2y from both sides, resulting in 8x = 100 - 2y. Next, we divide each term by 8 to solve for x, leading to x = (100 - 2y) / 8. Simplifying this expression gives x = 12.5 - 0.25y, which matches the provided answer. This shows how algebraic manipulation allows us to express x in terms of y.

Explanation

To isolate x in the equation 8x + 2y = 100, we first subtract 2y from both sides, resulting in 8x = 100 - 2y. Next, we divide each term by 8 to solve for x, leading to x = (100 - 2y) / 8. Simplifying this expression gives x = 12.5 - 0.25y, which matches the provided answer. This shows how algebraic manipulation allows us to express x in terms of y.

8) When solving a literal equation for a specific variable, which operation should be used to isolate x in 8x = 100 - 2y?

Subtract 8 from both sides

Multiply both sides by 8

Divide both sides by 8

Add 8 to both sides

To isolate the variable x in the equation 8x = 100 - 2y, you need to eliminate the coefficient of x. Since x is multiplied by 8, the appropriate operation is to divide both sides of the equation by 8. This operation simplifies the equation to x = (100 - 2y)/8, allowing you to solve for x directly.

Explanation

To isolate the variable x in the equation 8x = 100 - 2y, you need to eliminate the coefficient of x. Since x is multiplied by 8, the appropriate operation is to divide both sides of the equation by 8. This operation simplifies the equation to x = (100 - 2y)/8, allowing you to solve for x directly.