Simplify the algebraic expression. (1/5)(5x) + [(3y) + (- 3y)]...

Question

Simplify the algebraic expression. (1/5)(5x) + [(3y) + (- 3y)] - (-x)

Accepted Answer

Hi there. This problem we want to simplify this expression. It's not the first part of our expression is 2.7 times 21 X. The second part of our expression is this middle part four, Y plus negative 16 y times 1/4. And the final part of our expression is this minus negative six X. So we're going to simplify this in different parts. The first part states that we have to over seven Times x. So we have a fresh multiplication problem right here When we're multiplying fractions with an integer, we kind of want to imagine that there is a one underneath our x. The reason for that is we want to multiply the fraction to multiply a fraction. We multiply the enumerators and the denominators over into a new fraction. So what I mean by that is we would have to Times 21 x over seven. That's what which is how we would write our most efficient. So the little one that one there at the bottom kind of helps us imagine that they're both fractions in a sense. So we can go ahead and multiply this out two times 21 X. B 42 X seven times one is seven. No, We know that seven is invincible. It goes into 42. I mean so 42/7, we can simplify that even farther because those are coefficient coefficient is the number of MPX. 42 up for seven is just gonna be six x. No We can look at the middle section. The Middle Section says we have four white plus negative Y. Times 1/4. So we'll leave the four Y. For now we'll look at the negative 16 Y. Times 1/4 mom. Similarly to the last one will imagine that there is a one Underneath that 16 y. four y plus negative 16 Y over one times 1/4. So we can say we have four away Plus native 16 y times one Over one times 4. Which gives us or why Plus 9 - 16 y over four. Now We can simplify that. 16 y. And that four. So we get four y plus negative 16/4. We know is negative four. So it's negative for Y. Finally since we have a four Y plus a negative four Y. Those are going to cancel each other out. So or Y -4 way is going to go to zero. Now we can go ahead and look at the last section negative six X. And that is a minus negative six X. Actually so minus I use six X. Since we're subtracting a negative or sign is going to change to positive. So this turns from a minus 86 X. To just a six X. So I bring that down here Make it six x. Now we can check our sign one more time. So we have a six x. We're adding a zero And we're adding another six x. On the rights which means this answer. It's going to be equal to six X plus zero plus six X. Or 12 X. That means that our answer 12 X is going to be answer B. Okay. I hope that helped you solve the problem. Thank you for watching.

Simplify the algebraic expression. (1/5)(5x) + [(3y) + (- 3y)] - (-x)

Key Concepts

Distributive Property

Combining Like Terms

Negative Signs and Their Effects

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