How do you find the answer for 2/3x +15 = 17
The correct answer and explanation is:
To solve the equation: 23x+15=17\frac{2}{3}x + 15 = 17
we want to isolate the variable xx. Here’s the correct solution step-by-step:
Step 1: Subtract 15 from both sides
23x+15−15=17−15\frac{2}{3}x + 15 – 15 = 17 – 15 23x=2\frac{2}{3}x = 2
Step 2: Multiply both sides by the reciprocal of 23\frac{2}{3}
The reciprocal of 23\frac{2}{3} is 32\frac{3}{2}. So: (32)⋅23x=2⋅32\left(\frac{3}{2}\right) \cdot \frac{2}{3}x = 2 \cdot \frac{3}{2} x=3x = 3
✅ Final Answer: x=3x = 3
💬 Explanation (approx. 300 words):
This is a linear equation, which means the variable xx is not squared, inside a square root, or in the denominator. The goal of solving an equation like this is to isolate xx so we can find its value. We treat both sides of the equation equally, maintaining balance.
The original equation is: 23x+15=17\frac{2}{3}x + 15 = 17
This says that two-thirds of some number xx, increased by 15, equals 17. The first step is to undo the addition of 15 by subtracting 15 from both sides. This gets us closer to isolating xx. When we subtract 15, we simplify the equation to: 23x=2\frac{2}{3}x = 2
Now, 23x\frac{2}{3}x means “2/3 times xx.” To get just xx, we need to undo this multiplication. The best way to undo multiplying by 23\frac{2}{3} is to multiply both sides by its reciprocal, which is 32\frac{3}{2}. This is because: (32)⋅(23)=1\left(\frac{3}{2}\right) \cdot \left(\frac{2}{3}\right) = 1
Multiplying both sides: x=2⋅32=3x = 2 \cdot \frac{3}{2} = 3
Therefore, the value of xx that satisfies the equation is 3. You can check your answer by substituting x=3x = 3 back into the original equation: 23(3)+15=2+15=17\frac{2}{3}(3) + 15 = 2 + 15 = 17
✔️ Correct!