7x+1<4(x-2)

Question

solve 7x+1<4(x-2) please I need help with Algebra 1

Answer 1

Hello Shelby,

 

Your approach to solving this inequality would be the same as if it were a regular equation.

Because we have the value 4(x-2)...we want to distribute the 4 to remove the parenthesis.

 

4(x-2) = 4•x + 4•(-2) = 4x + -8 or 4x - 8 ... Now let's plug this back in.

7x+1 < 4x-8

 

Next you would perform the steps to solve for x... This means that we want all of our values with X on one side and values without X on the other.

First let's move the 4x to the left side with the 7x by subtracting it from the right side to remove it

(4x-4x = 0) and perform the same step on the left side

7x - 4x = 3x

 

Again the goal is to combine all values with X to one side and values without X to the other... So far we have:

3x+1 < -8    Can you guess the next step? If you guessed to move the 1 by subtracting it, you are correct!

Subtract the 1 from the left side (1 - 1 = 0)

Perform the same step on the right... That means we'll subtract 1 from the -8 on the right side.

-8 - 1 = -9   (If you're unfamiliar with this operation of integers, imagine that we owe someone $8 or -8. We then borrow another dollar or -1. This means we now owe them a total of 9 dollars.)

 

Now we have 3x < -9 ... Our next step is to solve for X (get X by itself) by dividing by the number in front of it, the 3.

 

3x÷3 = x (the 3÷3 cancels itself out or just equals 1 which we don't exactly need to write in front of X)

 

Again, for balance, what ever we do to one side, we must do to the other so we divide -9 by 3.

 

-9÷3 = -3   (With multiplication and division if your signs of 2 numbers are different, your answer is negative)

 

So x = -3 ... Here's your steps in order.

 

7x + 1 < 4(x - 2)

 

 7x + 1 < 4x - 8

-4x         -4x

 

 3x + 1 < -8

       - 1    -1

 

 3x < -9

  3      3

 

x = -3

Answer 2

7x + 1 < 4(x-2)

 

First let's distribute the 4

7x + 1 < 4x - 8

 

Now let's rearrange terms so that the variables (x) are on the left and the constants are on the right.

Subtract 4x from both sides

 

7x - 3x + 1 < -8

4x + 1 < -8

 

Subtract 1 from both sides

 

4x < -9

 

Finally, divide both sides by 4

 

x < -9/4