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tion 5: Solve each of the inequalities below \[ 4 x+3>2 x+11 \] (b) \( x+1 \geq 3 x-18 \) \( 13 x-12<3 x+13 \) (d) \( 7 x-5 \geq 3 x+11 \)

Ask by Floyd Evans. in Egypt
Mar 08,2025

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المتباينات والحلول: 1. \( 4x + 3 > 2x + 11 \) → \( x > 4 \) 2. \( x + 1 \geq 3x - 18 \) → \( x \leq 9.5 \) 3. \( 13x - 12 < 3x + 13 \) → \( x < 2.5 \) 4. \( 7x - 5 \geq 3x + 11 \) → \( x \geq 4 \)

Solución

Solve the inequality by following steps: - step0: Solve for \(x\): \(7x-5\geq 3x+11\) - step1: Move the expression to the left side: \(7x-3x\geq 11+5\) - step2: Add and subtract: \(4x\geq 11+5\) - step3: Add and subtract: \(4x\geq 16\) - step4: Divide both sides: \(\frac{4x}{4}\geq \frac{16}{4}\) - step5: Divide the numbers: \(x\geq 4\) Solve the equation \( 4x+3>2x+11 \). Solve the inequality by following steps: - step0: Solve for \(x\): \(4x+3>2x+11\) - step1: Move the expression to the left side: \(4x-2x>11-3\) - step2: Add and subtract: \(2x>11-3\) - step3: Add and subtract: \(2x>8\) - step4: Divide both sides: \(\frac{2x}{2}>\frac{8}{2}\) - step5: Divide the numbers: \(x>4\) Solve the equation \( x+1>=3x-18 \). Solve the inequality by following steps: - step0: Solve for \(x\): \(x+1\geq 3x-18\) - step1: Move the expression to the left side: \(x-3x\geq -18-1\) - step2: Add and subtract: \(-2x\geq -18-1\) - step3: Add and subtract: \(-2x\geq -19\) - step4: Change the signs: \(2x\leq 19\) - step5: Divide both sides: \(\frac{2x}{2}\leq \frac{19}{2}\) - step6: Divide the numbers: \(x\leq \frac{19}{2}\) Solve the equation \( 13x-12<3x+13 \). Solve the inequality by following steps: - step0: Solve for \(x\): \(13x-12<3x+13\) - step1: Move the expression to the left side: \(13x-3x<13+12\) - step2: Add and subtract: \(10x<13+12\) - step3: Add and subtract: \(10x<25\) - step4: Divide both sides: \(\frac{10x}{10}<\frac{25}{10}\) - step5: Divide the numbers: \(x<\frac{5}{2}\) إليك حلول المتباينات المعطاة: 1. **المتباينة الأولى**: \[ 4x + 3 > 2x + 11 \] الحل هو: \[ x > 4 \] 2. **المتباينة الثانية**: \[ x + 1 \geq 3x - 18 \] الحل هو: \[ x \leq \frac{19}{2} \] 3. **المتباينة الثالثة**: \[ 13x - 12 < 3x + 13 \] الحل هو: \[ x < \frac{5}{2} \] 4. **المتباينة الرابعة**: \[ 7x - 5 \geq 3x + 11 \] الحل هو: \[ x \geq 4 \] إذا كان لديك أي استفسارات أخرى، فلا تتردد في طرحها!

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Bonus Knowledge

To solve these inequalities, let’s break them down step by step. 1. For the first inequality, \( 4x + 3 > 2x + 11 \): - Subtract \( 2x \) from both sides: \( 2x + 3 > 11 \). - Then, subtract 3: \( 2x > 8 \). - Finally, divide by 2: \( x > 4 \). 2. For the second inequality, \( x + 1 \geq 3x - 18 \): - Subtract \( x \) from both sides: \( 1 \geq 2x - 18 \). - Add 18: \( 19 \geq 2x \). - Divide by 2: \( 9.5 \geq x \) or \( x \leq 9.5 \). 3. For the third inequality, \( 13x - 12 < 3x + 13 \): - Subtract \( 3x \) from both sides: \( 10x - 12 < 13 \). - Add 12: \( 10x < 25 \). - Divide by 10: \( x < 2.5 \). 4. For the fourth inequality, \( 7x - 5 \geq 3x + 11 \): - Subtract \( 3x \) from both sides: \( 4x - 5 \geq 11 \). - Add 5: \( 4x \geq 16 \). - Divide by 4: \( x \geq 4 \). In summary: - (a) \( x > 4 \) - (b) \( x \leq 9.5 \) - (c) \( x < 2.5 \) - (d) \( x \geq 4 \)

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