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torisob [31]
3 years ago
5

Solve the equation

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
5 0

Answer:

All real numbers; the simplification is described below.

Step-by-step explanation:

5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13

Let's keep in mind PEMDAS (the order of operations) to simplify and solve this. First, we'll distribute inside each set of parenthesis!

5(-3x) + 5(-2) -1(x) -1(-3) = -4(4x) -4(5) + 13

See how we've taken the outer term on the outside of the parenthesis and multiplied it to each term inside the parenthesis. Simplify further.

-15x - 10 - x + 3 = -16x - 20 + 13

Now we can combine like terms! I will bold the terms I am combining.

-15x - 10 - x + 3 = -16x - 20 + 13 (combining the x terms on the left)

-16x - 10 + 3 = -16x - 20 + 13 (combining the constants on both sides)

-16x - 7 = -16x - 7

Aha! It looks like we have an equation that's literally equal to itself. If we were to simplify this, or put in any number, we'd get that number equals itself. For example:

-16(1) - 7 = -16(1) - 7

-16 - 7 = -16 - 7

-21 = -21

Any number you put in here will make the equation true, so these lines must be the same line. That means the solution is all real numbers.

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