I had to solve (100-4x)/3=(5x+6)/(4)+6. I converted the fractions into twelfths, but from there I didn't know how to isolate the x's. How can you get them on there on side when they're partr of a fraction? Would you please be able to show me step by step how to do this? Thanks, Jaymie.
(100-4x)/3=(5x+6)/(4)+6
You have done the first step, found the LCM and convert them all over 12.
4(100-4x) 3(5x+6) + 72
---------= ------------
12 12
Now multiply both sides by 12 to remove the common denominator:
4(100-4x)=3(5x+6) + 72
The next step would be to expand and remove the parentheses using the distributivity properties of multiplication. I am sure you can handle the rest.
Post if you get stuck.
Of course, Jaymie! I'll be happy to guide you through the process step by step.
Step 1: Start by simplifying both sides of the equation.
To simplify the equation, you can start by distributing the fraction on the right-hand side:
(100 - 4x) / 3 = (5x + 6) / 4 + 6
Multiply the numerator and denominator of the fraction on the right-hand side by 3 to eliminate the fraction:
(100 - 4x) / 3 = (15x + 18) / 4 + 6
Now, let's eliminate the fraction on the right-hand side (5x + 6) by multiplying its numerator and denominator by 4:
(100 - 4x) / 3 = (15x + 18) / 4 + (6 * 4)
(100 - 4x) / 3 = (15x + 18) / 4 + 24
(100 - 4x) / 3 = (15x + 18) / 4 + 24/1
(100 - 4x) / 3 = (15x + 18) / 4 + 24/1
Step 2: Make the denominators equal.
To add or subtract fractions, you need to have a common denominator. In this case, the least common multiple (LCM) of 3 and 4 is 12. So, let's convert both fractions to have a denominator of 12.
Multiply the numerator and denominator of the first fraction by 4 to get a denominator of 12:
[(100 - 4x) * 4] / [(3 * 4)] = (15x + 18) / 4 + 24/1
(400 - 16x) / 12 = (15x + 18) / 4 + 24/1
Multiply the numerator and denominator of the second fraction by 3 to get a denominator of 12:
(400 - 16x) / 12 = [(15x + 18) * 3] / (4 * 3) + 24/1
(400 - 16x) / 12 = (45x + 54) / 12 + 24/1
Now, both fractions have a denominator of 12, so we can rewrite the equation as:
(400 - 16x) / 12 = (45x + 54 + 24) / 12
Step 3: Remove the denominators.
In order to simplify the equation further, you can eliminate the denominators by multiplying through by the common denominator (12).
Multiply both sides of the equation by 12:
12 * [(400 - 16x) / 12] = 12 * [(45x + 54 + 24) / 12]
Simplify the equation by canceling out the factors:
400 - 16x = 45x + 54 + 24
Step 4: Isolate the variable terms.
Now, we can rearrange the equation to isolate the x terms on one side and the constant terms on the other side.
First, let's combine the constant terms on the right-hand side:
400 - 16x = 45x + 78
Next, let's move the variable terms (with x) to one side and the constant terms to the other side. To do this, we can subtract 45x from both sides and add 16x to both sides:
400 - 16x - 45x = 45x + 78 - 45x - 16x
Simplifying both sides of the equation:
400 - 61x = 78 - x
Now, let's group the x terms and constant terms:
400 - 61x + x = 78
Simplifying further:
400 - 60x = 78
Step 5: Solve for x.
Finally, we can isolate the x term by subtracting 400 from both sides:
400 - 60x - 400 = 78 - 400
Simplifying both sides of the equation:
-60x = -322
To solve for x, divide both sides of the equation by -60:
x = -322 / -60
Simplifying further:
x ≈ 5.367
So, the solution to the equation (100-4x)/3=(5x+6)/(4)+6 is approximately x ≈ 5.367.