The image of the point (1, -2) after a rotation of 180° about the origin is:

Step 1: Simplify both sides of the equation.

5(−3x−2)−(x−3)=−4(4x+5)+13

5(−3x−2)+−1(x−3)=−4(4x+5)+13(Distribute the Negative Sign)

5(−3x−2)+−1x+(−1)(−3)=−4(4x+5)+13

5(−3x−2)+−x+3=−4(4x+5)+13

(5)(−3x)+(5)(−2)+−x+3=(−4)(4x)+(−4)(5)+13(Distribute)

−15x+−10+−x+3=−16x+−20+13

(−15x+−x)+(−10+3)=(−16x)+(−20+13)(Combine Like Terms)

−16x+−7=−16x+−7

−16x−7=−16x−7

Step 2: Add 16x to both sides.

−16x−7+16x=−16x−7+16x

−7=−7

Step 3: Add 7 to both sides.

−7+7=−7+7

0=0

• All real numbers are solutions

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.