<h3>
you should get:</h3>
x = 2
<h3>and here's how:</h3>
<u><em>* read to the bottom for a (shorter,) list format of the procedure used to get the solution for this question :))</em></u>
Assuming we are trying to find the value of x, we must isolate the variable x on one side whilst finding its value on the other. We should decide which side will have the variable x, and which will have x's value. I usually prefer to leave x on whichever has the overall highest x value. All of the x values are (+)2x on the left side and - 4x on the right side. Since 2x is greater than -4x, we will isolate x on the left side (2x - 3) and find x's value on the right side (9 - 4x).
Keep in mind that we will use the 'Line of Equality' rule for this inequality, which pretty much means that whatever we do to one side of the inequality, we must also do to the other. (Either side of the inequality is split up by the sign - in this case, the equal sign(=).)
We should start by removing the x value from the right side. We can do this by using the opposite operation as the one used for that number. On the right side, we have to cancel out -4x. Since -4x is also - 4x, or subtracting by 4x, we can eliminate this value by adding 4x. Due to the 'Line of Equality,' we also have to add 4x to the left side. 2x - 3 = 9 - 4x becomes 2x + 4x - 3 = 9 - 4x + 4x. 2x + 4x = 6x. -4x + 4x = 0 or 0x. Our new inequality is 6x - 3 = 9.
Next, we should remove the numerical value, or regular number (without any variables attached to it) from the left side. In order to cancel out the -3 from said side, we must change subtracting 3 to adding 3. Thanks to the ruling, we must do the same to the other side as well. So, we must add 3 to either side of the equation. 6x - 3 = 9 becomes 6x - 3 + 3 = 9 + 3. - 3 + 3 = 0. 9 + 3 = 12. Our new inequality is 6x = 12.
Then, we change 6x into a singular variable. In other words, we should change 6x to 1x or x (which are the same thing). 6x is the same thing as 6 * x. Since 6x is multiplying x by 6, we can create a single variable by dividing 6x by 6. The Line of Equality makes it so we have to divide the right side by 6 too. 6x = 12 becomes 6x ÷ 6 = 12 ÷ 6. 6x ÷ 6 = 1x or x. 12 ÷ 6 = 2. Our new inequality is x = 2. <em>(Since x is on the left side, and will be read first, there is no need to flip it to make it the same format as most inequalities are intended to be in.)</em>
Therefore, the value of x in the inequality 2x - 3 = 9 - 4x is 2, written accordingly in the equation x = 2.
<h3>List format timeeeee:</h3>
<u><em>- Line of equality makes us to the same to each side</em></u>
2x - 3 = 9 - 4x
<em>add 4x to each side</em>
2x + 4x - 3 = 9 - 4x + 4x <em>→ </em>6x - 3 = 9
6x - 3 = 9
<em>add 3 to each side</em>
6x - 3 + 3 = 9 + 3 <em>→ </em>6x = 12
6x = 12
<em>divide each side by 6</em>
6x ÷ 6 = 12 ÷ 6 <em>→ </em>x = 2
x = 2
<em>Therefore, the answer is x = 2.</em>
