Question

Solve: -8(x - 3) + 5x < 9(x + 12) This is Algebra 1

Answer 1

Answer:

The answer is x > -7

Step-by-step explanation:

The starting out equation is:

-8(x - 3) + 5x < 9(x + 12)

Once you've got your equation down, you have to remove the parentheses by doing distributive property, and multiplying the -8 by x and -3, [-8(x-3)] and the 9 by x and 12, [9(x + 12)]

Once you do that, you have something like this:

-8x + 24 + 5x < 9x + 108

Then you have to add like terms. That means adding -8x to the positive 5x, and only that since thats the only possible way.

-3x + 24 < 9x + 108

When that's over, you have to move the variable(in my case, 9x) to the left-hand side and change its sign:

-3x -9x + 24 < 108

You see that instead of positive 9x, like it was, it's now negative 9x since we changed its location.

And now do the same to the constant (in my case, 24) to the right-hand side. make sure to reverse its sign aswell, so now it's a negative 24. Now it looks a bit like this:

-3x -9x < 108 -24

Collect like terms (subtracting -9x by -3x, subtracting 108 by -24)

-12x < 84

Now that we isolated the variable, we have to divide it by -12.

KEEP IN MIND!!

When doing work like this, at some point you have to divide the variable by itself, and same thing to the other side. When the variable is a positive number and you're dividing by a positive number, DONT REVERSE THE GREATER/LESS (whatever you have) SIGN!!

When you are dividing by a negative number,

REVERSE THE SIGN!!

I always forgot this and got it wrong back then!!

Back to the lesson, itll look like this when dividing

-12x < 84

------ ------

-12x -12x

Once you divide it, you'll get this

x > -7

I hope this helped!

Answer 2

Answer:

x>−7

Step-by-step explanation:

left side:

-8(x-3)+5x

distribute -8 into (x-3)

-8x+24+5x

combine like terms

-3x+24

right side:

9(x+12)

distribute 9 into (x+12)

9x+108

-3x+24<9x+108

Subtract 24 on both sides

-3x< 9x+108-24

combine like terms

-3x<9x+84

Subtract 9x on both sides

-3x-9x<+84

combine like terms again

-12x<84

Multiply both sides by -1 (reverse the inequality)

(-12x)(-1)>84(-1)

12x>-84

divide both sides with 12

$\frac{12x}{12}>\frac{-84}{12}$

x>−7

hope this helps