Question

The product of a number, x, and seven is two less than 5 times the difference of the same number, x, and three

Please help

Answer 1

Answer: -8.5 or -17/2

Step-by-step explanation: you have to put the info into an equation. product of a number x and 7 is 7x. two less than mean subtracting two and 5 times the difference of x and 3 translates to 5(x-3). Once put into an equation, it'll look like 7x = 5(x-3) - 2. Now solve this equation for x and you'll end up with -8.5 in decimals or -17/2 in fractions.

Answer 2

`\sf x = (-17 )/( 2) \textsf{or} -8.5`

Explanation:

Let's translate the given statement into an algebraic equation.

"The product of a number, x, and seven" can be represented as 7x.

"Two less than 5 times the difference of the same number, x, and three" can be represented as 5(x - 3) - 2.

Now, we can set up the equation:

`\sf 7x = 5(x - 3) - 2`

Next, we'll solve for x:

Distribute the 5 on the right side:

`\sf 7x = 5x - 15 - 2`

Combine like terms on the right side:

`\sf 7x = 5x - 17`

Subtract 5x from both sides to isolate the variable x:

`\sf 7x - 5x = -17`

`\sf 2x = -17`

Divide both sides by 2 to solve for x:

`\sf ((2x) )/(2) = (-17 )/( 2)`

`\sf x = (-17 )/( 2) \textsf{or} -8.5`

So, the solution to the equation is:

`\sf x = (-17 )/( 2) \textsf{or} -8.5`