How do you go about solving this word problem?

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x = integer

x+ 1 = next (consecutive) integer

The greater integer (x+1) is (=) twice the smaller (2x)

x + 1 = 2x + 15

Put x's together and terms together on opposite sides

1 + x - x = 2x + 15 - x

1 = x + 15

-14 = x

x+ 1 = -13.

Check x + 1 = 2x + 15

substitute for x+1 and X

-13 = 2(-14) + 15

-13 = -28 + 15

-13 = -13 Correct on both sides. There are your two answers. I substituted -14 for X and -13 for x+1.

Katherine P. | Shoreview Area Math Tutoring and Test PrepShoreview Area Math Tutoring and Test Pr...

This is an algebra word problem that can be solved by setting up a system of equations. Stay with me! It only sounds complicated, but we will make it easy.

We have two consecutive integers, let's call them x and y.

Let's say y comes after x, so that means y = x+1 (consecutive numbers are in sequence, like counting, each number is 1 more than the number before it)

Now let's use our other clue from the problem. The larger number is 15 more than twice the smaller.

y is the larger number, and that is 15 more than 2 times the smaller number (x)

y = 15 + 2x

Ok, now let's use substitution.

y = x+1, so we plug that into our equation.

x + 1 = 15 + 2x

Get the variable terms on the left and the constant terms on the right.

x + 1 = 15 + 2x

- 2x -2x

-x + 1 = 15

- 1 -1

-x = 14

*-1 *-1

x = -14

Plug our value of x back into our definition of y.

y = -14 + 1

y = -13

So we have -14 and -13. This makes sense because integers can be negative, -14 and -13 are consecutive, and if we multiply the smaller number (-14) by 2, then add 15, we get -13. Our answer checks out!

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