solve 3 X/4 – 7 /4 = 5 x + 12
The Correct Answer and Explanation is:
Given Equation:
3×4−74=5x+12\frac{3x}{4} – \frac{7}{4} = 5x + 12
Step 1: Eliminate fractions
Multiply every term by 4 to eliminate the denominators: 4(3×4−74)=4(5x+12)4 \left( \frac{3x}{4} – \frac{7}{4} \right) = 4(5x + 12) 3x−7=20x+483x – 7 = 20x + 48
Step 2: Get all x terms on one side
Subtract 3x3x from both sides: −7=17x+48-7 = 17x + 48
Step 3: Move constants to the other side
Subtract 48 from both sides: −55=17x-55 = 17x
Step 4: Solve for x
x=−5517x = \frac{-55}{17}
✅ Final Answer:
x=−5517\boxed{x = \frac{-55}{17}}
✍️ Explanation
To solve the equation 3×4−74=5x+12\frac{3x}{4} – \frac{7}{4} = 5x + 12, we begin by eliminating the fractions to simplify our work. Both fractional terms on the left have a denominator of 4, so we multiply every term in the equation by 4. This clears the denominators: 4(3×4−74)=4(5x+12)⇒3x−7=20x+484 \left( \frac{3x}{4} – \frac{7}{4} \right) = 4(5x + 12) \Rightarrow 3x – 7 = 20x + 48
This equation is much simpler. Next, we isolate the variable. To move all x terms to one side, we subtract 3x3x from both sides: −7=17x+48-7 = 17x + 48
Now, we isolate the term with x by removing the constant on the right side. Subtract 48 from both sides: −55=17x-55 = 17x
Finally, divide both sides by 17 to solve for x: x=−5517x = \frac{-55}{17}
This fraction is already in simplest form, and there’s no need to convert it to a decimal unless specifically required. Leaving it as an improper fraction is acceptable in algebra.
This problem illustrates how important it is to first eliminate fractions to simplify an equation. Then, using inverse operations (subtracting and dividing), we rearrange the equation step by step until x is isolated. Always check that each step maintains the balance of the equation. In the end, careful arithmetic and logical steps lead us to the correct solution: x=−5517\boxed{x = \frac{-55}{17}}.
