Question

challenge find a description this equation represents. of the numbers 1, 2, 3, 4, and 5, which are solutions to the equation?
5x - 13 = 2

a. if you subtract thirteen times a number from five, you get 2.

b. five more than thirteen times a number is 2.

c. if you add thirteen to five times a number, you get 2.

d. if you subtract thirteen from five times a number, you get 2.

e. thirteen more than five times a number is 2.

f. if you subtract five from thirteen times a number, you get 2.

g. five less than thirteen times a number is 2.

h. thirteen less than five times a number is 2.

click to select your answer(s) and then click check answer.
1 part remaining

Explanation:

Step1: Analyze the equation \(5x - 13 = 2\)

The left - hand side of the equation is \(5x-13\), which can be interpreted as "thirteen less than five times a number \(x\)" or "if you subtract thirteen from five times a number, you get 2".

Step2: Evaluate each option

- Option A: The expression for "subtract thirteen times a number from five" would be \(5 - 13x\), not \(5x - 13\), so A is incorrect.
- Option B: The expression for "five more than thirteen times a number" is \(13x + 5\), not \(5x-13\), so B is incorrect.
- Option C: The expression for "add thirteen to five times a number" is \(5x + 13\), not \(5x - 13\), so C is incorrect.
- Option D: The expression \(5x-13\) can be described as "subtract thirteen from five times a number", and the equation is \(5x - 13=2\), so the description "If you subtract thirteen from five times a number, you get 2" matches.
- Option E: The expression for "thirteen more than five times a number" is \(5x + 13\), not \(5x - 13\), so E is incorrect.
- Option F: The expression for "subtract five from thirteen times a number" is \(13x-5\), not \(5x - 13\), so F is incorrect.
- Option G: The expression for "five less than thirteen times a number" is \(13x - 5\), not \(5x - 13\), so G is incorrect.
- Option H: The phrase "thirteen less than five times a number" is equivalent to \(5x-13\), and the equation \(5x - 13 = 2\) can be described as "Thirteen less than five times a number is 2", so H also matches. But let's check the solution of the equation \(5x-13 = 2\).
Solve \(5x-13=2\):
Add 13 to both sides: \(5x-13 + 13=2 + 13\), so \(5x=15\).
Divide both sides by 5: \(x = 3\). Now we check which numbers from 1,2,3,4,5 are solutions. When \(x = 3\), \(5\times3-13=15 - 13 = 2\), so \(x = 3\) is a solution. But first, for the description part, both D and H are correct descriptions. But looking at the options again, D says "If you subtract thirteen from five times a number, you get 2" and H says "Thirteen less than five times a number is 2". Both are correct descriptions of the equation \(5x - 13=2\). But let's re - check the equation interpretation. The equation \(5x-13 = 2\) can be read as "five times a number minus thirteen equals two", which can be rephrased as "subtract thirteen from five times a number, you get 2" (option D) or "thirteen less than five times a number is 2" (option H). But let's check the wording again.

Wait, let's re - examine the equation structure. \(5x-13\) is "five times \(x\) minus thirteen". So "subtract thirteen from five times a number" (D) and "thirteen less than five times a number" (H) are both correct. But let's check the original equation's description.

The equation \(5x-13 = 2\):

For option D: "If you subtract thirteen from five times a number, you get 2" - this is a procedural description (using the action of subtraction).

For option H: "Thirteen less than five times a number is 2" - this is a descriptive (comparative) description. Both are correct. But let's check the options again. The problem first asks for a description of the equation and then which numbers are solutions. But for the description part, both D and H are correct. But let's check the options again. The equation \(5x-13 = 2\) can be described as in D and H. But let's check the solution:

Solve \(5x-13=2\):

\(5x=2 + 13=15\)

\(x = 3\)

So among 1,2,3,4,5, \(x = 3\) is the solution. But first, for the description, both D and H are correct. But let's check the options again. The option D: "If you subtract thirteen from five times a number, you get 2" and option H: "Thirteen less than five times a number is 2" are both correct descriptions. But maybe the question considers the wording. Let's see the equation \(5x-13 = 2\). The left - hand side is \(5x-13\), which is "five times \(x\) minus thirteen". So "subtract thirteen from five times a number" (D) and "thirteen less than five times a number" (H) are both correct. But let's check the options again. The problem is a multiple - choice for the description and then the solution. But the first part is to find the description. Let's assume that both D and H are correct descriptions, but let's check the options again. Wait, maybe I made a mistake. Let's re - read the options:

Option D: "If you subtract thirteen from five times a number, you get 2"

Option H: "Thirteen less than five times a number is 2"

Both are correct. But let's check the equation \(5x-13 = 2\). The solution is \(x = 3\), which is in the set \(\{1,2,3,4,5\}\).

But for the description part, let's see the original equation \(5x-13 = 2\). The phrase "five times a number" is \(5x\), "subtract thirteen from it" gives \(5x - 13\), and it equals 2, so D is a correct description. Also, "thirteen less than five times a number" is \(5x-13\), and it equals 2, so H is also correct. But maybe the question considers the wording. Let's check the options again. The problem is from a math problem, likely in the sub - field of Algebra.

Answer:

For the description part: D. If you subtract thirteen from five times a number, you get 2; H. Thirteen less than five times a number is 2. And the solution to the equation \(5x - 13=2\) is \(x = 3\), so among 1,2,3,4,5, the solution is 3. But for the description options, both D and H are correct. If we have to choose one, D is a more procedural description and H is a more descriptive (comparative) description. But according to the options, let's check the equation again. The equation is \(5x-13 = 2\), so the description "If you subtract thirteen from five times a number, you get 2" (D) and "Thirteen less than five times a number is 2" (H) are both correct. And the solution is \(x = 3\), so the number from 1,2,3,4,5 that is a solution is 3.

But the first part is to find the description. Let's assume the question is first about the description. So the correct description options are D and H. And the solution is \(x = 3\).