Which of the following equations has the same solution as the equation x + 1/2 = −1/4 ?

Answer 1

To determine which equation has the same solution as \( x + \frac{1}{2} = -\frac{1}{4} \), we first need to solve the original equation for \( x \).

1. Start with the original equation: \[ x + \frac{1}{2} = -\frac{1}{4} \]

2. Subtract \( \frac{1}{2} \) from both sides: \[ x = -\frac{1}{4} - \frac{1}{2} \]

3. To perform the subtraction, convert \( \frac{1}{2} \) to a fraction with a denominator of 4: \[ \frac{1}{2} = \frac{2}{4} \]

4. Now, substitute it back into the equation: \[ x = -\frac{1}{4} - \frac{2}{4} = -\frac{3}{4} \]

So the solution to the equation \( x + \frac{1}{2} = -\frac{1}{4} \) is \( x = -\frac{3}{4} \).

To find an equivalent equation that has the same solution, you can either manipulate the original equation or use equivalent transformations. Here are examples of possible equivalent equations:

• Multiply both sides of the equation \( x + \frac{1}{2} = -\frac{1}{4} \) by any non-zero number.
• Add or subtract the same quantity from both sides.
• Change the equation to a form of \( ax + b = c \).

If you provide the list of equations, I can help identify which one has the same solution \( x = -\frac{3}{4} \).

Answer 2

x + 1/2 = 5/4
x plus Start Fraction 1 over 2 End Fraction equals Start Fraction 5 over 4 End Fraction

x − 1/4 = 1
x minus Start Fraction 1 over 4 End Fraction equals 1

x + 1.5 = 0.75
x plus 1.5 equals 0.75

x − 0.70 = −0.05

Answer 3

To find which of the given equations has the same solution as \( x + \frac{1}{2} = -\frac{1}{4} \) (where we previously solved it and got \( x = -\frac{3}{4} \)), let's solve each of the provided equations for \( x \) and check if they yield \( -\frac{3}{4} \).

1. Equation: \( x + \frac{1}{2} = \frac{5}{4} \)

   Subtract \( \frac{1}{2} \) from both sides: \[ x = \frac{5}{4} - \frac{1}{2} \] Convert \( \frac{1}{2} \) to a fraction with a denominator of 4: \[ x = \frac{5}{4} - \frac{2}{4} = \frac{3}{4} \]

2. Equation: \( x - \frac{1}{4} = 1 \)

   Add \( \frac{1}{4} \) to both sides: \[ x = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \]

3. Equation: \( x + 1.5 = 0.75 \)

   Subtract \( 1.5 \) from both sides (convert \( 1.5 \) to a fraction): \[ 1.5 = \frac{3}{2} \quad \text{(or 1.5 = 1.5)} \] \[ x = 0.75 - 1.5 = -0.75 \] Convert \( -0.75 \) to a fraction: \[ x = -\frac{3}{4} \]

4. Equation: \( x - 0.70 = -0.05 \)

   Add \( 0.70 \) to both sides: \[ x = -0.05 + 0.70 = 0.65 \] Convert \( 0.65 \) to a fraction: \[ x = \frac{65}{100} = \frac{13}{20} \]

Summary of the results:

• From \( x + \frac{1}{2} = \frac{5}{4} \), we get \( x = \frac{3}{4} \).
• From \( x - \frac{1}{4} = 1 \), we get \( x = \frac{5}{4} \).
• From \( x + 1.5 = 0.75 \), we get \( x = -\frac{3}{4} \).
• From \( x - 0.70 = -0.05 \), we get \( x = \frac{13}{20} \).

Conclusion: The equation \( x + 1.5 = 0.75 \) has the same solution \( x = -\frac{3}{4} \) as the original equation \( x + \frac{1}{2} = -\frac{1}{4} \).

Answer 4

Nick bought groceries for n dollars. He had a coupon for $15.50 off. He paid $34.63 including tax for the groceries he purchased. Which equation represents the original cost of groceries Nick bought? What was this amount?(1 point)
Responses

n + 15.50 = 34.63; the original cost of the groceries Nick bought was $19.13.
n plus 15.50 equals 34.63 ; the original cost of the groceries Nick bought was $19.13.

n + 34.63 = 15.50; the original cost of the groceries Nick bought was $50.13.
n plus 34.63 equals 15.50 ; the original cost of the groceries Nick bought was $50.13.

n − 34.63 = 15.50; the original cost of the groceries Nick bought was $19.13.
n minus 34.63 equals 15.50 ; the original cost of the groceries Nick bought was $19.13.

n − 15.50 = 34.63; the original cost of the groceries Nick bought was $50.13.

Answer 5

Let's break down the problem step by step.

1. Understanding the situation: Nick bought groceries at an original price of \( n \) dollars. He applied a coupon that gave him a discount of $15.50. After applying the coupon, he paid $34.63 for the groceries.

2. Setting up the equation: The equation to represent the situation can be set up based on the relationship between the original price \( n \), the discount from the coupon, and the amount he paid: \[ n - 15.50 = 34.63 \] This means that the original cost of the groceries minus the coupon amount equals the amount paid.

3. Solving for \( n \): To find \( n \), we can rearrange the equation: \[ n = 34.63 + 15.50 \] Now, performing the addition: \[ n = 50.13 \]

So the original cost of the groceries Nick bought was $50.13.

Conclusion:

The correct equation that represents the original cost of groceries Nick bought is: \[ n - 15.50 = 34.63 \] And the original cost was $50.13.

Thus, the correct response from your list is:

• n − 15.50 = 34.63; the original cost of the groceries Nick bought was $50.13.

Answer 6

Mela wants to buy a pair of shoes that costs $40.99 including tax. She gives the cashier $50 . Which equation can be used to find the amount of change, c , Mela receives? How much is her change?(1 point)
Responses

c − 40.99 = 50; Mela receives $90.99 in change.
c minus 40.99 equals 50 ; Mela receives $90.99 in change.

c + 50 = 40.99; Mela receives $9.01 in change.
c plus 50 equals 40.99 ; Mela receives $9.01 in change.

c − 50 = 40.99; Mela receives $90.99 in change.
c minus 50 equals 40.99 ; Mela receives $90.99 in change.

c + 40.99 = 50; Mela receives $9.01 in change.

Answer 7

To determine the amount of change \( c \) Mela receives after buying a pair of shoes for $40.99 and giving the cashier $50, we can set up the equation based on the relationship between the cash given, the cost of the shoes, and the change received.

1. Understanding the situation:

   • Mela pays $40.99 for the shoes.
   • She gives the cashier $50.
   • The change she receives can be calculated by subtracting the cost of the shoes from the amount she gave.

2. Setting up the equation: The equation can be set up as follows: \[ c = 50 - 40.99 \] We can rearrange it in the form of an equation: \[ c + 40.99 = 50 \]

3. Solving for \( c \): Now, calculate the change she receives: \[ c = 50 - 40.99 = 9.01 \]

Conclusion:

The correct equation that can be used to find the amount of change \( c \) Mela receives is: \[ c + 40.99 = 50 \] And Mela receives $9.01 in change.

Thus, the correct response from your list is:

• c + 40.99 = 50; Mela receives $9.01 in change.

Answer 8

Which equation has a different solution than the rest?(1 point)
Responses

x/4=−1
Start Fraction x over 4 End Fraction equals negative 1

x/−2=2
Start Fraction x over negative 2 equals 2

−12x=48
negative 12x equals 48

16x=64

Answer 9

To determine which equation has a different solution from the rest, let's solve each equation for \( x \).

1. Equation: \(\frac{x}{4} = -1\)

   Multiply both sides by 4: \[ x = -1 \times 4 = -4 \]

2. Equation: \(\frac{x}{-2} = 2\)

   Multiply both sides by \(-2\): \[ x = 2 \times -2 = -4 \]

3. Equation: \(-12x = 48\)

   Divide both sides by \(-12\): \[ x = \frac{48}{-12} = -4 \]

4. Equation: \(16x = 64\)

   Divide both sides by 16: \[ x = \frac{64}{16} = 4 \]

Summary of solutions:

• From \(\frac{x}{4} = -1\), we get \(x = -4\).
• From \(\frac{x}{-2} = 2\), we get \(x = -4\).
• From \(-12x = 48\), we get \(x = -4\).
• From \(16x = 64\), we get \(x = 4\).

Conclusion:

The first three equations have the solution \(x = -4\). The last equation \(16x = 64\) has a different solution, \(x = 4\).

Thus, the equation that has a different solution than the rest is:

• \(16x = 64\).

Answer 10

Which of the following equations has a solution of −11/4 ?(1 point)
Responses

−2x=2/11
negative 2 x equals Start Fraction 2 over 11 End Fraction

−2x=11/2
negative 2 x equals Start Fraction 11 over 2 End Fraction

1/2x=−11
Start Fraction 1 over 2 End Fraction x equals negative 11

−1/2x=112

Answer 11

To find which of the following equations has a solution of \(-\frac{11}{4}\), we will solve each equation for \(x\) and check if any of them equal \(-\frac{11}{4}\).

1. Equation: \(-2x = \frac{2}{11}\)

   Divide both sides by \(-2\): \[ x = \frac{2/11}{-2} = \frac{2}{-22} = -\frac{1}{11} \]

2. Equation: \(-2x = \frac{11}{2}\)

   Divide both sides by \(-2\): \[ x = \frac{11/2}{-2} = \frac{11}{-4} = -\frac{11}{4} \] (This equals the solution we want!)

3. Equation: \(\frac{1}{2}x = -11\)

   Multiply both sides by 2 to eliminate the fraction: \[ x = -11 \times 2 = -22 \]

4. Equation: \(-\frac{1}{2}x = 112\)

   Multiply both sides by \(-2\) to solve for \(x\): \[ x = 112 \times -2 = -224 \]

Summary of results:

• The first equation yields \(x = -\frac{1}{11}\).
• The second equation yields \(x = -\frac{11}{4}\).
• The third equation yields \(x = -22\).
• The fourth equation yields \(x = -224\).

Conclusion:

The equation that has a solution of \(-\frac{11}{4}\) is:

• \(-2x = \frac{11}{2}\).