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3. หแเก้อสมการโดยใช้สมบัติการบวก และเขียนกราฟแลดงคำตอบของอสมการนั้น \( 3.12 x-5
Ask by Long Tyler. in Thailand
Feb 21,2025

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### คำตอบของอสมการ 1. **อสมการที่ 1: \( 3.12 x - 5 < x + 2 \)** - \( x < \frac{175}{53} \) 2. **อสมการที่ 2: \( 3.25 x + 4 \leq 4 x + 3 \)** - \( x \geq \frac{4}{3} \) ### กราฟแสดงคำตอบ - **อสมการที่ 1**: \( x < \frac{175}{53} \) มีเส้นประที่ \( \frac{175}{53} \) และ shading ไปทางซ้าย - **อสมการที่ 2**: \( x \geq \frac{4}{3} \) มีจุดที่ \( \frac{4}{3} \) และ shading ไปทางขวา กราฟจะแสดงผลลัพธ์ตามที่ระบุข้างต้น

Solución

Solve the inequality by following steps: - step0: Solve for \(x\): \(3.25x+4\leq 4x+3\) - step1: Move the expression to the left side: \(3.25x-4x\leq 3-4\) - step2: Add and subtract: \(-0.75x\leq 3-4\) - step3: Add and subtract: \(-0.75x\leq -1\) - step4: Change the signs: \(0.75x\geq 1\) - step5: Divide both sides: \(\frac{0.75x}{0.75}\geq \frac{1}{0.75}\) - step6: Divide the numbers: \(x\geq \frac{4}{3}\) Solve the equation \( 3.12 x-5 0 1 2 3 4 5 6 7 8 9 10 ● -------------------> ``` - ● แสดงถึง \( \frac{4}{3} \) (รวม) - --- แสดงถึง \( \frac{175}{53} \) (ไม่รวม)

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The Deep Dive

เริ่มต้นจากอสมการแรก \( 3.12x - 5 < x + 2 \) เราสามารถจัดรูปให้อยู่ในรูปของ \( x \) ได้โดยการบวก \( 5 \) และลบ \( x \) ทั้งสองข้าง จะได้ \( 3.12x - x < 2 + 5 \) หรือ \( 2.12x < 7 \) จากนั้นแบ่งทั้งสองข้างด้วย \( 2.12 \) จะได้ \( x < \frac{7}{2.12} \) ซึ่งประมาณ \( x < 3.30 \) สำหรับอสมการที่สอง \( 3.25x + 4 \leq 4x + 3 \) เราจะจัดรูปโดยการลบ \( 4x \) และ \( 4 \) ทั้งสองข้าง จะได้ \( 3.25x - 4x \leq 3 - 4 \) ซึ่งคือ \( -0.75x \leq -1 \) หรือเมื่อแบ่งทั้งสองข้างด้วย \( -0.75 \) เราต้องกลับอสมการเป็น \( x \geq \frac{1}{0.75} \) ประมาณ \( x \geq \frac{4}{3} \) หรือ \( x \geq 1.33 \) เมื่อเขียนกราฟ เราสามารถแทนค่า \( x < 3.30 \) ด้วยกราฟตั้งแต่ -∞ ถึง 3.30 และกราฟ \( x \geq 1.33 \) จะเริ่มจาก 1.33 ไปจนถึง +∞ โดยเฉพาะจุดที่ 1.33 จะเป็นวงกลมที่ไม่เต็ม (เปิด) แสดงว่ารวมทั้งค่าที่มากกว่าแต่ไม่รวม 1.33.

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