Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−4=2x+6(1 point)

7 answers

To solve for x in the equation 5(2x+2)-4=2x+6, we first distribute the 5 on the left side:

10x + 10 - 4 = 2x + 6

Simplify the equation:

10x + 6 = 2x + 6

Move all terms involving x to one side of the equation:

10x - 2x = 6 - 6

8x = 0

Divide by 8:

x = 0

Therefore, the equation has only one solution, x = 0.
Sammie and her 3 cousins split their winnings from bingo evenly. She paid $25 to get a ride home. If she had $475 when she got home, how much money did they win altogether?(1 point) Responses $133.33 $133.33 $125 $125 $112.50 $112.50 $2,000
Let's denote the amount of money they won altogether as x.

If they split the winnings evenly, Sammie receives $\frac{1}{4}$ of the total amount (since there are 4 people including her).

She paid $25 for a ride home, so she actually received $475 - $25 = $450 from the winnings.

We can set up an equation to represent this:

$\frac{1}{4}x = 450$

Multiplying both sides by 4 to solve for x:

$x = 450 \times 4$

$x = 1800$

Therefore, they won $1800 altogether. The closest option provided is $2000, which is not correct. The correct answer is $1800.
theres no 1800
I apologize for missing that. Let's revisit the calculation to ensure we have the correct answer.

With the information given, including Sammie paying $25 and having $475 when she got home, we can infer that the total amount they won was $475 + $25 = $500.

Therefore, the correct response from the options provided is $125, as they won $500 in total and split it evenly among the 4 cousins. Each received $125.
Solve the following linear equation for x . Then check your answer. Show all your steps for solving and checking. 5x+8+x=32 (4 points)
To solve the linear equation 5x + 8 + x = 32, we need to simplify the equation step by step:

1. Combine like terms:
5x + x = 6x

The equation becomes:
6x + 8 = 32

2. Subtract 8 from both sides to isolate the variable term:
6x = 32 - 8
6x = 24

3. Divide by 6 to solve for x:
x = 24 /6
x = 4

Therefore, x = 4 is the solution to the linear equation 5x + 8 + x = 32.

To check the solution, substitute x = 4 back into the original equation:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
28 + 4 = 32
32 = 32

The checked solution is correct since both sides of the equation are equal, confirming that x = 4 is the correct solution.