75.1k views
0 votes
Write an equation and solve to find the numbers and show work.

9. Doubling the difference between a number and 4 is 6 more than the number.
10. Five less than the opposite of a number is three times the sum of the number and -7.

User EraftYps
by
8.4k points

1 Answer

2 votes

9. Let's start by defining the variable.

Let's say the number we're trying to find is "x".

Now, let's translate the problem into an equation:

2(x - 4) = x + 6

We can simplify this equation by distributing the 2:

2x - 8 = x + 6

Next, let's isolate the variable on one side of the equation by subtracting x from both sides:

x - 8 = 6

Finally, we can solve for x by adding 8 to both sides:

x = 14

Therefore, the number we're looking for is 14.

10. Let's start by defining the variable.

Let's say the number we're trying to find is "x".

Now, let's translate the problem into an equation:

-(x) - 5 = 3(x + (-7))

We can simplify the right side of the equation by first simplifying the expression inside the parentheses:

-(x) - 5 = 3(x - 7)

Next, we can distribute the 3:

-(x) - 5 = 3x - 21

Let's isolate the variable on one side of the equation by adding x to both sides:

-(x) + x - 5 = 3x + x - 21

Simplifying the left side of the equation:

-5 = 4x - 21

Now, we can isolate the variable by adding 21 to both sides:

-5 + 21 = 4x

Simplifying the left side of the equation:

16 = 4x

Finally, we can solve for x by dividing both sides by 4:

x = 4

Therefore, the number we're looking for is 4.

User Aseyboldt
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.